A deep reinforcement learning method to control chaos synchronization between two identical chaotic systems
We propose a model-free deep reinforcement learning method for controlling the synchronization between two identical chaotic systems, one target and one reference. By interacting with the target and the reference, the agent continuously optimizes its strategy of applying perturbations to the target...
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| Published in: | Chaos, solitons and fractals Vol. 174; p. 113809 |
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| Main Authors: | , , , |
| Format: | Journal Article |
| Language: | English |
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Elsevier Ltd
01.09.2023
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| ISSN: | 0960-0779 |
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| Abstract | We propose a model-free deep reinforcement learning method for controlling the synchronization between two identical chaotic systems, one target and one reference. By interacting with the target and the reference, the agent continuously optimizes its strategy of applying perturbations to the target to synchronize the trajectory of the target with the reference. This method is different from previous chaos synchronization methods. It requires no prior knowledge of the chaotic systems. We apply the deep reinforcement learning method to several typical chaotic systems (Lorenz system, Rössler system, Chua circuit and Logistic map) and its efficiency of controlling synchronization between the target and the reference is demonstrated. Especially, we find that a single learned agent can be used to control the chaos synchronization for different chaotic systems. We also find that the method works well in controlling chaos synchronization even when only incomplete information of the state variables of the target and the reference can be obtained.
•A model-free deep reinforcement learning method for controlling chaos synchronization is proposed.•The efficiency of controlling synchronization is demonstrated.•A single learned agent can be used to control the chaos synchronization for different chaotic systems.•The method works well even when only incomplete information of the state variables of the chaotic systems can be obtained. |
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| AbstractList | We propose a model-free deep reinforcement learning method for controlling the synchronization between two identical chaotic systems, one target and one reference. By interacting with the target and the reference, the agent continuously optimizes its strategy of applying perturbations to the target to synchronize the trajectory of the target with the reference. This method is different from previous chaos synchronization methods. It requires no prior knowledge of the chaotic systems. We apply the deep reinforcement learning method to several typical chaotic systems (Lorenz system, Rössler system, Chua circuit and Logistic map) and its efficiency of controlling synchronization between the target and the reference is demonstrated. Especially, we find that a single learned agent can be used to control the chaos synchronization for different chaotic systems. We also find that the method works well in controlling chaos synchronization even when only incomplete information of the state variables of the target and the reference can be obtained.
•A model-free deep reinforcement learning method for controlling chaos synchronization is proposed.•The efficiency of controlling synchronization is demonstrated.•A single learned agent can be used to control the chaos synchronization for different chaotic systems.•The method works well even when only incomplete information of the state variables of the chaotic systems can be obtained. |
| ArticleNumber | 113809 |
| Author | Yang, Junzhong Li, Haihong Cheng, Haoxin Dai, Qionglin |
| Author_xml | – sequence: 1 givenname: Haoxin surname: Cheng fullname: Cheng, Haoxin – sequence: 2 givenname: Haihong surname: Li fullname: Li, Haihong email: haihongli@bupt.edu.cn – sequence: 3 givenname: Qionglin orcidid: 0000-0001-6120-4689 surname: Dai fullname: Dai, Qionglin – sequence: 4 givenname: Junzhong surname: Yang fullname: Yang, Junzhong |
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| Cites_doi | 10.1142/S0218127497000455 10.1103/PhysRevE.49.4882 10.1063/1.5128909 10.1103/PhysRevLett.65.3211 10.1103/PhysRevE.56.5265 10.1063/1.166451 10.1109/MSP.2017.2743240 10.1063/1.166265 10.1103/PhysRevE.53.4528 10.1063/1.2183734 10.1016/S0960-0779(02)00585-4 10.1103/PhysRevLett.76.1816 10.1103/PhysRevA.42.1946 10.1007/s11071-021-06302-9 10.3390/app11188589 10.1103/PhysRevE.55.5285 10.1103/PhysRevE.50.1874 10.1063/1.2759438 10.1038/nature14236 10.1109/ACCESS.2019.2956816 10.1177/0278364913495721 10.1063/1.1938627 10.1007/s10462-021-10061-9 10.1109/ACCESS.2021.3056037 10.1016/S0960-0779(02)00005-X 10.1016/S0370-1573(99)00096-4 10.1063/1.2193684 10.1016/j.physleta.2005.08.060 10.1038/nature14539 10.1103/PhysRevLett.64.821 10.1103/PhysRevLett.74.5028 10.3367/UFNe.0179.200912c.1281 10.1016/S0370-1573(02)00137-0 10.1088/1009-1963/13/2/008 10.1063/1.5117263 10.1007/s10462-020-09938-y 10.1103/PhysRevE.51.980 10.1126/science.aar6404 10.1063/5.0002047 10.1016/j.chaos.2003.12.088 10.1103/PhysRevE.53.6566 10.1103/PhysRevLett.76.1804 10.1038/nature04275 10.1016/j.physleta.2010.05.024 10.1039/D0CP03580G 10.1103/PhysRevLett.78.4193 10.1016/j.cnsns.2021.105708 10.1016/j.neunet.2014.09.003 10.1038/nature24270 10.1016/j.physd.2021.133068 10.1016/0960-0779(95)00046-1 10.1109/TITS.2021.3054625 10.1063/1.5120370 10.1103/PhysRevE.72.016205 10.1103/PhysRevA.101.053851 10.1016/S0375-9601(98)00086-3 10.1016/S0960-0779(96)00156-7 10.1186/s13662-021-03320-0 10.1103/PhysRevE.50.1894 10.1109/TSMCC.2007.913919 10.1016/j.neunet.2020.02.008 10.3390/biology11091317 10.1142/S0218127402004668 10.1103/PhysRevLett.64.1196 |
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| Keywords | Deep reinforcement learning Chaos synchronization Model-free method Continuous control |
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| References | Feki (b19) 2003; 18 Rosenblum, Pikovsky, Kurths (b29) 1996; 76 Tao (b74) 2006; 348 Heagy, Carroll, Pecora (b23) 1994; 50 Bukov, Day, Sels, Weinberg, Polkovnikov, Mehta (b60) 2018; 8 Moon, Baik, Seo (b20) 2021; 96 Koronovskii, Moskalenko, Hramov (b7) 2009; 52 Calışır, Pehlivanoğlu (b68) 2019 Moskalenko, Koronovskii, Hramov (b8) 2010; 374 Yu (b71) 1997; 8 Malescio (b42) 1996; 53 Boutayeb, Darouach, Rafaralahy (b75) 2002; 49 Li, Liao, Zhang (b22) 2005; 15 Guan, Li, Lai (b24) 2006; 16 Xiao, Xu, Li, Tang (b28) 2007; 17 Fox (b73) 1990; 42 Rosenblum, Pikovsky, Kurths (b21) 1997; 78 Du, Ding (b50) 2021; 54 Agostinelli, Hocquet, Singh, Baldi (b65) 2018; 11100 Hu, Zhang, Tian, Wang (b4) 2019; 7 Fang, Hao (b70) 1996; 7 Pecora, Carroll (b35) 1990; 64 Suykens, Vandewalle (b38) 1997; 7 Jahanshahi, Yousefpour, Munoz-Pacheco, Kacar, Pham, Alsaadi (b12) 2020; 383 Ali, Fang (b43) 1997; 55 Zhang, You, Lü (b2) 2020; 101 Lin, Chen (b27) 2006; 16 . Vaseghi, Mobayen, Hashemi, Fekih (b11) 2021; 9 Schulman J, Wolski F, Dhariwal P, Radford A, Klimov O. Proximal policy optimization algorithms Biferale, Bonaccorso, Buzzicotti, Leoni, Gustavsson (b59) 2019; 29 Yu, Zhang (b40) 2004; 22 Frolov, Maksimenko, Lüttjohann, Koronovskii, Hramov (b46) 2019; 29 Le, Rathour, Yamazaki, Luu, Savvides (b54) 2022; 55 Xiu, Zhou, Zhao, Xu (b14) 2021; 104 Lin, He (b26) 2005; 15 Yu, Zhang, Liu (b13) 2020; 2020 Han, Ding, Du, Lei (b64) 2021; 428 Silver, Schrittwieser, Simonyan (b51) 2017; 550 Kiran, Sobh, Talpaert, Mannion, Sallab, Yogamani (b55) 2022; 23 Argyris, Syvridis, Larger (b5) 2006; 438 Martín-Guerrero, Lamata (b56) 2021; 11 Gadaleta, Dangelmayr (b57) 1999; 9 Krylov, Dylov, Rosenblum (b58) 2020; 30 Chen, Yin, Huang, Yuan, Zheng, Yin (b10) 2020; 125 Vashishtha, Verma (b62) 2020; 30 Mnih, Kavukcuoglu, Silver (b47) 2015; 518 Kocarev, Parlitz (b37) 1995; 74 Arulkumaran, Deisenroth, Brundage, Bharath (b48) 2017; 34 Zhang, Xu, Wang (b3) 2020; 22 Baptista (b6) 1998; 240 Lecun, Bengio, Hinton (b67) 2015; 521 Abarbanel, Rulkov, Sushchik (b34) 1996; 53 Lai, Grebogi (b41) 1994; 50 Pikovsky, Zaks, Rosenblum, Osipov, Kurths (b31) 1997; 7 Kocarev, Parlitz (b33) 1996; 76 Boccaletti, Kurths, Osipov, Valladares, Zhou (b25) 2002; 366 Boccaletti, Grebogi, Lai, Mancini, Maza (b17) 2000; 329 Bucci, Semeraro, Allauzen, Wisniewski, Cordier, Mathelin (b63) 2019; 475 Gecow, Iantovics, Tez (b1) 2022; 11 Li, Lin, Gao, Tang, Deng, Ni (b9) 2020; 82 Silver, Hubert, Schrittwieser (b53) 2018; 362 Fösel, Tighineanu, Weiss (b61) 2018; 8 Ditto, Rauseo, Spano (b18) 1990; 65 Awrejcewicz, Calvisi (b72) 2002; 12 Rulkov, Sushchik, Tsimring, Abarbanel (b32) 1995; 51 Liaw, Tung (b45) 1997; 56 Baleanu, Sajjadi, Asad, Jajarmi, Estiri (b15) 2021; 2021 Guan, Lai, Wei (b30) 2005; 72 Buşoniu, Babuška, Schutter (b49) 2008; 38 Lü, Zhou, Zhang (b39) 2002; 14 Li, Zhou, Xu (b44) 2004; 13 Murali, Lakshmanan (b36) 1994; 49 Schmidhuber (b66) 2015; 61 Ott, Grebogi, Yorke (b16) 1990; 64 Kober, Bagnell, Peters (b52) 2013; 32 Argyris (10.1016/j.chaos.2023.113809_b5) 2006; 438 Koronovskii (10.1016/j.chaos.2023.113809_b7) 2009; 52 Ott (10.1016/j.chaos.2023.113809_b16) 1990; 64 Du (10.1016/j.chaos.2023.113809_b50) 2021; 54 Xiao (10.1016/j.chaos.2023.113809_b28) 2007; 17 Suykens (10.1016/j.chaos.2023.113809_b38) 1997; 7 Xiu (10.1016/j.chaos.2023.113809_b14) 2021; 104 Frolov (10.1016/j.chaos.2023.113809_b46) 2019; 29 Krylov (10.1016/j.chaos.2023.113809_b58) 2020; 30 Bucci (10.1016/j.chaos.2023.113809_b63) 2019; 475 Jahanshahi (10.1016/j.chaos.2023.113809_b12) 2020; 383 Murali (10.1016/j.chaos.2023.113809_b36) 1994; 49 10.1016/j.chaos.2023.113809_b69 Arulkumaran (10.1016/j.chaos.2023.113809_b48) 2017; 34 Baptista (10.1016/j.chaos.2023.113809_b6) 1998; 240 Li (10.1016/j.chaos.2023.113809_b44) 2004; 13 Rosenblum (10.1016/j.chaos.2023.113809_b21) 1997; 78 Lin (10.1016/j.chaos.2023.113809_b27) 2006; 16 Vashishtha (10.1016/j.chaos.2023.113809_b62) 2020; 30 Martín-Guerrero (10.1016/j.chaos.2023.113809_b56) 2021; 11 Pikovsky (10.1016/j.chaos.2023.113809_b31) 1997; 7 Kocarev (10.1016/j.chaos.2023.113809_b33) 1996; 76 Chen (10.1016/j.chaos.2023.113809_b10) 2020; 125 Yu (10.1016/j.chaos.2023.113809_b40) 2004; 22 Lin (10.1016/j.chaos.2023.113809_b26) 2005; 15 Kocarev (10.1016/j.chaos.2023.113809_b37) 1995; 74 Zhang (10.1016/j.chaos.2023.113809_b3) 2020; 22 Agostinelli (10.1016/j.chaos.2023.113809_b65) 2018; 11100 Moon (10.1016/j.chaos.2023.113809_b20) 2021; 96 Yu (10.1016/j.chaos.2023.113809_b13) 2020; 2020 Boccaletti (10.1016/j.chaos.2023.113809_b17) 2000; 329 Boccaletti (10.1016/j.chaos.2023.113809_b25) 2002; 366 Boutayeb (10.1016/j.chaos.2023.113809_b75) 2002; 49 Fösel (10.1016/j.chaos.2023.113809_b61) 2018; 8 Hu (10.1016/j.chaos.2023.113809_b4) 2019; 7 Gadaleta (10.1016/j.chaos.2023.113809_b57) 1999; 9 Lü (10.1016/j.chaos.2023.113809_b39) 2002; 14 Rosenblum (10.1016/j.chaos.2023.113809_b29) 1996; 76 Abarbanel (10.1016/j.chaos.2023.113809_b34) 1996; 53 Vaseghi (10.1016/j.chaos.2023.113809_b11) 2021; 9 Kiran (10.1016/j.chaos.2023.113809_b55) 2022; 23 Moskalenko (10.1016/j.chaos.2023.113809_b8) 2010; 374 Le (10.1016/j.chaos.2023.113809_b54) 2022; 55 Lecun (10.1016/j.chaos.2023.113809_b67) 2015; 521 Tao (10.1016/j.chaos.2023.113809_b74) 2006; 348 Silver (10.1016/j.chaos.2023.113809_b53) 2018; 362 Zhang (10.1016/j.chaos.2023.113809_b2) 2020; 101 Rulkov (10.1016/j.chaos.2023.113809_b32) 1995; 51 Li (10.1016/j.chaos.2023.113809_b22) 2005; 15 Fang (10.1016/j.chaos.2023.113809_b70) 1996; 7 Silver (10.1016/j.chaos.2023.113809_b51) 2017; 550 Schmidhuber (10.1016/j.chaos.2023.113809_b66) 2015; 61 Bukov (10.1016/j.chaos.2023.113809_b60) 2018; 8 Mnih (10.1016/j.chaos.2023.113809_b47) 2015; 518 Ditto (10.1016/j.chaos.2023.113809_b18) 1990; 65 Guan (10.1016/j.chaos.2023.113809_b24) 2006; 16 Yu (10.1016/j.chaos.2023.113809_b71) 1997; 8 Fox (10.1016/j.chaos.2023.113809_b73) 1990; 42 Kober (10.1016/j.chaos.2023.113809_b52) 2013; 32 Gecow (10.1016/j.chaos.2023.113809_b1) 2022; 11 Feki (10.1016/j.chaos.2023.113809_b19) 2003; 18 Ali (10.1016/j.chaos.2023.113809_b43) 1997; 55 Li (10.1016/j.chaos.2023.113809_b9) 2020; 82 Han (10.1016/j.chaos.2023.113809_b64) 2021; 428 Heagy (10.1016/j.chaos.2023.113809_b23) 1994; 50 Calışır (10.1016/j.chaos.2023.113809_b68) 2019 Awrejcewicz (10.1016/j.chaos.2023.113809_b72) 2002; 12 Liaw (10.1016/j.chaos.2023.113809_b45) 1997; 56 Malescio (10.1016/j.chaos.2023.113809_b42) 1996; 53 Biferale (10.1016/j.chaos.2023.113809_b59) 2019; 29 Guan (10.1016/j.chaos.2023.113809_b30) 2005; 72 Lai (10.1016/j.chaos.2023.113809_b41) 1994; 50 Buşoniu (10.1016/j.chaos.2023.113809_b49) 2008; 38 Baleanu (10.1016/j.chaos.2023.113809_b15) 2021; 2021 Pecora (10.1016/j.chaos.2023.113809_b35) 1990; 64 |
| References_xml | – volume: 2020 year: 2020 ident: b13 article-title: Secure communication scheme based on a new 5D multistable four-wing memristive hyperchaotic system with disturbance inputs publication-title: Complexity – volume: 18 start-page: 141 year: 2003 ident: b19 article-title: An adaptive chaos synchronization scheme applied to secure communication publication-title: Chaos Solitons Fractals – volume: 104 start-page: 789 year: 2021 ident: b14 article-title: Memristive hyperchaos secure communication based on sliding mode control publication-title: Nonlinear Dynam – volume: 29 year: 2019 ident: b46 article-title: Feed-forward artificial neural network provides data-driven inference of functional publication-title: Chaos – volume: 428 year: 2021 ident: b64 article-title: Control and anti-control of chaos based on the moving largest Lyapunov exponent using reinforcement learning publication-title: Physica D – volume: 23 start-page: 4909 year: 2022 ident: b55 article-title: Deep reinforcement learning for autonomous driving: A survey publication-title: IEEE Trans Intell Transp Syst – volume: 29 year: 2019 ident: b59 article-title: Zermelo’s problem: optimal point-to-point navigation in 2D turbulent flows using reinforcement learning publication-title: Chaos – volume: 374 start-page: 2925 year: 2010 ident: b8 article-title: Generalized synchronization of chaos for secure communication: remarkable stability to noise publication-title: Phys Lett A – volume: 53 start-page: 4528 year: 1996 ident: b34 article-title: Generalized synchronization of chaos: the auxiliary system approach publication-title: Phys Rev E – volume: 362 start-page: 1140 year: 2018 ident: b53 article-title: A general reinforcement learning algorithm that masters chess, shogi and go through self-play publication-title: Science – volume: 16 year: 2006 ident: b24 article-title: Chaotic synchronization through coupling strategies publication-title: Chaos – volume: 550 start-page: 354 year: 2017 ident: b51 article-title: Mastering the game of go without human knowledge publication-title: Nature – volume: 14 start-page: 529 year: 2002 ident: b39 article-title: Chaos synchronization between linearly coupled chaotic systems publication-title: Chaos Solitons Fractals – volume: 51 start-page: 980 year: 1995 ident: b32 article-title: Generalized synchronization of chaos in directionally coupled chaotic systems publication-title: Phys Rev E – volume: 49 start-page: 3 year: 2002 ident: b75 article-title: Generalized state-space observers for chaotic synchronization and secure communication publication-title: IEEE Trans Circuits Syst I-Regul Pap – volume: 7 start-page: 665 year: 1997 ident: b38 article-title: Master–slave synchronization of Lur’e systems publication-title: Int J Bifurcation Chaos – volume: 30 year: 2020 ident: b62 article-title: Restoring chaos using deep reinforcement learning publication-title: Chaos – volume: 9 start-page: 25911 year: 2021 ident: b11 article-title: Fast reaching finite time synchronization approach for chaotic systems with application in medical image encryption publication-title: IEEE Access – volume: 55 start-page: 2733 year: 2022 ident: b54 article-title: Deep reinforcement learning in computer vision: A comprehensive survey publication-title: Artif Intell Rev – volume: 7 year: 2019 ident: b4 article-title: Chaotic dynamics in asymmetric rock–paper–scissors games publication-title: IEEE Access – volume: 9 start-page: 775 year: 1999 ident: b57 article-title: Optimal chaos control through reinforcement learning publication-title: Chaos – volume: 7 start-page: 680 year: 1997 ident: b31 article-title: Phase synchronization of chaotic oscillations in terms of periodic orbits publication-title: Chaos – volume: 38 start-page: 156 year: 2008 ident: b49 article-title: A comprehensive survey of multiagent reinforcement learning publication-title: IEEE Trans Syst Man Cybern C – volume: 32 start-page: 1238 year: 2013 ident: b52 article-title: Reinforcement learning in robotics: A survey publication-title: Int J Robot Res – reference: Schulman J, Wolski F, Dhariwal P, Radford A, Klimov O. Proximal policy optimization algorithms, – volume: 52 start-page: 1213 year: 2009 ident: b7 article-title: On the use of chaotic synchronization for secure communication publication-title: Phys-Usp – volume: 65 start-page: 3211 year: 1990 ident: b18 article-title: Experimental control of chaos publication-title: Phys Rev Lett – volume: 64 start-page: 821 year: 1990 ident: b35 article-title: Synchronization in chaotic systems publication-title: Phys Rev Lett – volume: 11100 start-page: 298 year: 2018 ident: b65 article-title: From reinforcement learning to deep reinforcement learning: An overview publication-title: Lect Notes Artif Intell – volume: 78 start-page: 4193 year: 1997 ident: b21 article-title: From phase to lag synchronization in coupled chaotic oscillators publication-title: Phys Rev Lett – volume: 76 start-page: 1804 year: 1996 ident: b29 article-title: Phase synchronization of chaotic oscillators publication-title: Phys Rev Lett – volume: 383 year: 2020 ident: b12 article-title: A new fractional-order hyperchaotic memristor oscillator: dynamic analysis, robust adaptive synchronization, and its application to voice encryption publication-title: Appl Math Comput – volume: 53 start-page: 6566 year: 1996 ident: b42 article-title: Synchronization of the Lorenz system through continuous feedback control publication-title: Phys Rev E – volume: 22 start-page: 27896 year: 2020 ident: b3 article-title: The dynamic and thermodynamic origin of dissipative chaos: chemical Lorenz system publication-title: Phys Chem Chem Phys – volume: 15 year: 2005 ident: b22 article-title: Impulsive synchronization of chaotic systems publication-title: Chaos – volume: 30 year: 2020 ident: b58 article-title: Reinforcement learning for suppression of collective activity in oscillatory ensembles publication-title: Chaos – volume: 50 start-page: 1894 year: 1994 ident: b41 article-title: Synchronization of spatiotemporal chaotic systems by feedback control publication-title: Phys Rev E – volume: 13 start-page: 168 year: 2004 ident: b44 article-title: Chaos synchronization based on intermittent state observer publication-title: Chin J Phys – volume: 54 start-page: 3215 year: 2021 ident: b50 article-title: A survey on multi-agent deep reinforcement learning: from the perspective of challenges and applications publication-title: Artif Intell Rev – volume: 15 year: 2005 ident: b26 article-title: Complete synchronization of the noise-perturbed Chua’s circuits publication-title: Chaos – volume: 96 year: 2021 ident: b20 article-title: Chaos synchronization in generalized Lorenz systems and an application to image encryption publication-title: Commun Nonlinear Sci Numer Simul – volume: 518 start-page: 529 year: 2015 ident: b47 article-title: Human-level control through deep reinforcement learning publication-title: Nature – volume: 82 year: 2020 ident: b9 article-title: Security-enhanced bidirectional communication based on a long-distance chaos synchronization system with double optical feedback, 13th international congress on image and signal processing publication-title: BioMed Eng Inform – volume: 521 start-page: 436 year: 2015 ident: b67 article-title: Deep learning publication-title: Nature – volume: 61 start-page: 85 year: 2015 ident: b66 article-title: Deep learning in neural networks: an overview publication-title: Neural Netw – volume: 11 start-page: 1317 year: 2022 ident: b1 article-title: Cancer and chaos and the complex network model of a multicellular organism publication-title: Biology-Basel – volume: 438 start-page: 343 year: 2006 ident: b5 article-title: Chaos-based communications at high bit rates using commercial fibre-optic links publication-title: Nature – volume: 8 year: 2018 ident: b61 article-title: Reinforcement learning with neural networks for quantum feedback publication-title: Phys Rev X – volume: 12 start-page: 671 year: 2002 ident: b72 article-title: Mechanical models of Chua’s circuit publication-title: Int J Bifurcation Chaos – volume: 50 start-page: 1874 year: 1994 ident: b23 article-title: Synchronous chaos in coupled oscillator systems publication-title: Phys Rev E – volume: 17 year: 2007 ident: b28 article-title: Adaptive complete synchronization of chaotic dynamical network with unknown and mismatched parameters publication-title: Chaos – volume: 34 start-page: 26 year: 2017 ident: b48 article-title: Deep reinforcement learning publication-title: IEEE Signal Process Mag – volume: 348 start-page: 201 year: 2006 ident: b74 article-title: Dislocated feedback synchronization of Lorenz chaotic system publication-title: Phys Lett A – volume: 64 start-page: 1196 year: 1990 ident: b16 article-title: Controlling chaos publication-title: Phys Rev Lett – volume: 42 start-page: 1946 year: 1990 ident: b73 article-title: Master equation for the logistic map publication-title: Phys Rev A – volume: 329 start-page: 103 year: 2000 ident: b17 article-title: The control of chaos: theory and applications publication-title: Phys Rep – volume: 22 start-page: 189 year: 2004 ident: b40 article-title: The synchronization of linearly bidirectional coupled chaotic systems publication-title: Chaos Solitons Fractals – volume: 56 start-page: 5265 year: 1997 ident: b45 article-title: Analysis and observer design in synchronization via a state feedback control method publication-title: Phys Rev E – volume: 366 start-page: 1 year: 2002 ident: b25 article-title: The synchronization of chaotic systems publication-title: Phys Rep – year: 2019 ident: b68 article-title: Model tabanlı olmayan pekiştirmeli öğrenme algoritmaları üzerine i̇nceleme model-free reinforcement learning algorithms: A survey publication-title: 27th Signal processing and communications applications conference – volume: 16 year: 2006 ident: b27 article-title: Using white noise to enhance synchronization of coupled chaotic systems publication-title: Chaos – volume: 11 start-page: 8589 year: 2021 ident: b56 article-title: Reinforcement learning and physics publication-title: Appl Sci – volume: 240 start-page: 50 year: 1998 ident: b6 article-title: Cryptography with chaos publication-title: Phys Lett A – volume: 76 start-page: 1816 year: 1996 ident: b33 article-title: Generalized synchronization, predictability, and equivalence of unidirectionally coupled dynamical systems publication-title: Phys Rev Lett – volume: 8 year: 2018 ident: b60 article-title: Reinforcement learning in different phases of quantum control publication-title: Phys Rev X – volume: 8 start-page: 1577 year: 1997 ident: b71 article-title: Variable structure control approach for controlling chaos publication-title: Chaos Solitons Fractals – volume: 125 start-page: 174 year: 2020 ident: b10 article-title: Chaos in fractional-order discrete neural networks with application to image encryption publication-title: Neural Netw – reference: . – volume: 101 year: 2020 ident: b2 article-title: Intermittent chaos in cavity optomechanics publication-title: Phys Rev A – volume: 74 start-page: 5028 year: 1995 ident: b37 article-title: General approach for chaotic synchronization with applications to communication publication-title: Phys Rev Lett – volume: 475 start-page: 2231 year: 2019 ident: b63 article-title: Control of chaotic systems by deep reinforcement learning publication-title: Proc R Soc Lond Ser A Math Phys Eng Sci – volume: 72 year: 2005 ident: b30 article-title: Phase synchronization between two essentially different chaotic systems publication-title: Phys Rev E – volume: 2021 start-page: 157 year: 2021 ident: b15 article-title: Hyperchaotic behaviors, optimal control, and synchronization of a nonautonomous cardiac conduction system publication-title: Adv Differential Equations – volume: 49 start-page: 4882 year: 1994 ident: b36 article-title: Drive-response scenario of chaos synchronization in identical nonlinear systems publication-title: Phys Rev E – volume: 7 start-page: 217 year: 1996 ident: b70 article-title: Symbolic dynamics of the Lorenz equations publication-title: Chaos Solitons Fractals – volume: 55 start-page: 5285 year: 1997 ident: b43 article-title: Synchronization of chaos and hyperchaos using linear and nonlinear feedback functions publication-title: Phys Rev E – volume: 7 start-page: 665 year: 1997 ident: 10.1016/j.chaos.2023.113809_b38 article-title: Master–slave synchronization of Lur’e systems publication-title: Int J Bifurcation Chaos doi: 10.1142/S0218127497000455 – volume: 49 start-page: 4882 year: 1994 ident: 10.1016/j.chaos.2023.113809_b36 article-title: Drive-response scenario of chaos synchronization in identical nonlinear systems publication-title: Phys Rev E doi: 10.1103/PhysRevE.49.4882 – volume: 30 year: 2020 ident: 10.1016/j.chaos.2023.113809_b58 article-title: Reinforcement learning for suppression of collective activity in oscillatory ensembles publication-title: Chaos doi: 10.1063/1.5128909 – volume: 65 start-page: 3211 year: 1990 ident: 10.1016/j.chaos.2023.113809_b18 article-title: Experimental control of chaos publication-title: Phys Rev Lett doi: 10.1103/PhysRevLett.65.3211 – volume: 56 start-page: 5265 year: 1997 ident: 10.1016/j.chaos.2023.113809_b45 article-title: Analysis and observer design in synchronization via a state feedback control method publication-title: Phys Rev E doi: 10.1103/PhysRevE.56.5265 – volume: 9 start-page: 775 year: 1999 ident: 10.1016/j.chaos.2023.113809_b57 article-title: Optimal chaos control through reinforcement learning publication-title: Chaos doi: 10.1063/1.166451 – volume: 82 year: 2020 ident: 10.1016/j.chaos.2023.113809_b9 article-title: Security-enhanced bidirectional communication based on a long-distance chaos synchronization system with double optical feedback, 13th international congress on image and signal processing publication-title: BioMed Eng Inform – volume: 383 year: 2020 ident: 10.1016/j.chaos.2023.113809_b12 article-title: A new fractional-order hyperchaotic memristor oscillator: dynamic analysis, robust adaptive synchronization, and its application to voice encryption publication-title: Appl Math Comput – volume: 34 start-page: 26 year: 2017 ident: 10.1016/j.chaos.2023.113809_b48 article-title: Deep reinforcement learning publication-title: IEEE Signal Process Mag doi: 10.1109/MSP.2017.2743240 – volume: 7 start-page: 680 year: 1997 ident: 10.1016/j.chaos.2023.113809_b31 article-title: Phase synchronization of chaotic oscillations in terms of periodic orbits publication-title: Chaos doi: 10.1063/1.166265 – volume: 11100 start-page: 298 year: 2018 ident: 10.1016/j.chaos.2023.113809_b65 article-title: From reinforcement learning to deep reinforcement learning: An overview publication-title: Lect Notes Artif Intell – volume: 53 start-page: 4528 year: 1996 ident: 10.1016/j.chaos.2023.113809_b34 article-title: Generalized synchronization of chaos: the auxiliary system approach publication-title: Phys Rev E doi: 10.1103/PhysRevE.53.4528 – volume: 16 year: 2006 ident: 10.1016/j.chaos.2023.113809_b27 article-title: Using white noise to enhance synchronization of coupled chaotic systems publication-title: Chaos doi: 10.1063/1.2183734 – volume: 18 start-page: 141 year: 2003 ident: 10.1016/j.chaos.2023.113809_b19 article-title: An adaptive chaos synchronization scheme applied to secure communication publication-title: Chaos Solitons Fractals doi: 10.1016/S0960-0779(02)00585-4 – volume: 76 start-page: 1816 year: 1996 ident: 10.1016/j.chaos.2023.113809_b33 article-title: Generalized synchronization, predictability, and equivalence of unidirectionally coupled dynamical systems publication-title: Phys Rev Lett doi: 10.1103/PhysRevLett.76.1816 – volume: 42 start-page: 1946 year: 1990 ident: 10.1016/j.chaos.2023.113809_b73 article-title: Master equation for the logistic map publication-title: Phys Rev A doi: 10.1103/PhysRevA.42.1946 – volume: 104 start-page: 789 year: 2021 ident: 10.1016/j.chaos.2023.113809_b14 article-title: Memristive hyperchaos secure communication based on sliding mode control publication-title: Nonlinear Dynam doi: 10.1007/s11071-021-06302-9 – volume: 11 start-page: 8589 year: 2021 ident: 10.1016/j.chaos.2023.113809_b56 article-title: Reinforcement learning and physics publication-title: Appl Sci doi: 10.3390/app11188589 – volume: 49 start-page: 3 year: 2002 ident: 10.1016/j.chaos.2023.113809_b75 article-title: Generalized state-space observers for chaotic synchronization and secure communication publication-title: IEEE Trans Circuits Syst I-Regul Pap – volume: 55 start-page: 5285 year: 1997 ident: 10.1016/j.chaos.2023.113809_b43 article-title: Synchronization of chaos and hyperchaos using linear and nonlinear feedback functions publication-title: Phys Rev E doi: 10.1103/PhysRevE.55.5285 – volume: 50 start-page: 1874 year: 1994 ident: 10.1016/j.chaos.2023.113809_b23 article-title: Synchronous chaos in coupled oscillator systems publication-title: Phys Rev E doi: 10.1103/PhysRevE.50.1874 – volume: 2020 year: 2020 ident: 10.1016/j.chaos.2023.113809_b13 article-title: Secure communication scheme based on a new 5D multistable four-wing memristive hyperchaotic system with disturbance inputs publication-title: Complexity – volume: 17 year: 2007 ident: 10.1016/j.chaos.2023.113809_b28 article-title: Adaptive complete synchronization of chaotic dynamical network with unknown and mismatched parameters publication-title: Chaos doi: 10.1063/1.2759438 – volume: 518 start-page: 529 year: 2015 ident: 10.1016/j.chaos.2023.113809_b47 article-title: Human-level control through deep reinforcement learning publication-title: Nature doi: 10.1038/nature14236 – volume: 15 year: 2005 ident: 10.1016/j.chaos.2023.113809_b22 article-title: Impulsive synchronization of chaotic systems publication-title: Chaos – volume: 7 year: 2019 ident: 10.1016/j.chaos.2023.113809_b4 article-title: Chaotic dynamics in asymmetric rock–paper–scissors games publication-title: IEEE Access doi: 10.1109/ACCESS.2019.2956816 – volume: 32 start-page: 1238 year: 2013 ident: 10.1016/j.chaos.2023.113809_b52 article-title: Reinforcement learning in robotics: A survey publication-title: Int J Robot Res doi: 10.1177/0278364913495721 – volume: 8 year: 2018 ident: 10.1016/j.chaos.2023.113809_b60 article-title: Reinforcement learning in different phases of quantum control publication-title: Phys Rev X – volume: 15 year: 2005 ident: 10.1016/j.chaos.2023.113809_b26 article-title: Complete synchronization of the noise-perturbed Chua’s circuits publication-title: Chaos doi: 10.1063/1.1938627 – volume: 55 start-page: 2733 year: 2022 ident: 10.1016/j.chaos.2023.113809_b54 article-title: Deep reinforcement learning in computer vision: A comprehensive survey publication-title: Artif Intell Rev doi: 10.1007/s10462-021-10061-9 – volume: 9 start-page: 25911 year: 2021 ident: 10.1016/j.chaos.2023.113809_b11 article-title: Fast reaching finite time synchronization approach for chaotic systems with application in medical image encryption publication-title: IEEE Access doi: 10.1109/ACCESS.2021.3056037 – volume: 14 start-page: 529 year: 2002 ident: 10.1016/j.chaos.2023.113809_b39 article-title: Chaos synchronization between linearly coupled chaotic systems publication-title: Chaos Solitons Fractals doi: 10.1016/S0960-0779(02)00005-X – volume: 329 start-page: 103 year: 2000 ident: 10.1016/j.chaos.2023.113809_b17 article-title: The control of chaos: theory and applications publication-title: Phys Rep doi: 10.1016/S0370-1573(99)00096-4 – volume: 16 year: 2006 ident: 10.1016/j.chaos.2023.113809_b24 article-title: Chaotic synchronization through coupling strategies publication-title: Chaos doi: 10.1063/1.2193684 – volume: 348 start-page: 201 year: 2006 ident: 10.1016/j.chaos.2023.113809_b74 article-title: Dislocated feedback synchronization of Lorenz chaotic system publication-title: Phys Lett A doi: 10.1016/j.physleta.2005.08.060 – volume: 521 start-page: 436 year: 2015 ident: 10.1016/j.chaos.2023.113809_b67 article-title: Deep learning publication-title: Nature doi: 10.1038/nature14539 – year: 2019 ident: 10.1016/j.chaos.2023.113809_b68 article-title: Model tabanlı olmayan pekiştirmeli öğrenme algoritmaları üzerine i̇nceleme model-free reinforcement learning algorithms: A survey – volume: 64 start-page: 821 year: 1990 ident: 10.1016/j.chaos.2023.113809_b35 article-title: Synchronization in chaotic systems publication-title: Phys Rev Lett doi: 10.1103/PhysRevLett.64.821 – volume: 74 start-page: 5028 year: 1995 ident: 10.1016/j.chaos.2023.113809_b37 article-title: General approach for chaotic synchronization with applications to communication publication-title: Phys Rev Lett doi: 10.1103/PhysRevLett.74.5028 – volume: 8 year: 2018 ident: 10.1016/j.chaos.2023.113809_b61 article-title: Reinforcement learning with neural networks for quantum feedback publication-title: Phys Rev X – volume: 52 start-page: 1213 year: 2009 ident: 10.1016/j.chaos.2023.113809_b7 article-title: On the use of chaotic synchronization for secure communication publication-title: Phys-Usp doi: 10.3367/UFNe.0179.200912c.1281 – volume: 366 start-page: 1 year: 2002 ident: 10.1016/j.chaos.2023.113809_b25 article-title: The synchronization of chaotic systems publication-title: Phys Rep doi: 10.1016/S0370-1573(02)00137-0 – volume: 13 start-page: 168 year: 2004 ident: 10.1016/j.chaos.2023.113809_b44 article-title: Chaos synchronization based on intermittent state observer publication-title: Chin J Phys doi: 10.1088/1009-1963/13/2/008 – volume: 29 year: 2019 ident: 10.1016/j.chaos.2023.113809_b46 article-title: Feed-forward artificial neural network provides data-driven inference of functional publication-title: Chaos doi: 10.1063/1.5117263 – volume: 54 start-page: 3215 year: 2021 ident: 10.1016/j.chaos.2023.113809_b50 article-title: A survey on multi-agent deep reinforcement learning: from the perspective of challenges and applications publication-title: Artif Intell Rev doi: 10.1007/s10462-020-09938-y – volume: 51 start-page: 980 year: 1995 ident: 10.1016/j.chaos.2023.113809_b32 article-title: Generalized synchronization of chaos in directionally coupled chaotic systems publication-title: Phys Rev E doi: 10.1103/PhysRevE.51.980 – volume: 362 start-page: 1140 year: 2018 ident: 10.1016/j.chaos.2023.113809_b53 article-title: A general reinforcement learning algorithm that masters chess, shogi and go through self-play publication-title: Science doi: 10.1126/science.aar6404 – volume: 30 year: 2020 ident: 10.1016/j.chaos.2023.113809_b62 article-title: Restoring chaos using deep reinforcement learning publication-title: Chaos doi: 10.1063/5.0002047 – volume: 22 start-page: 189 year: 2004 ident: 10.1016/j.chaos.2023.113809_b40 article-title: The synchronization of linearly bidirectional coupled chaotic systems publication-title: Chaos Solitons Fractals doi: 10.1016/j.chaos.2003.12.088 – volume: 53 start-page: 6566 year: 1996 ident: 10.1016/j.chaos.2023.113809_b42 article-title: Synchronization of the Lorenz system through continuous feedback control publication-title: Phys Rev E doi: 10.1103/PhysRevE.53.6566 – volume: 76 start-page: 1804 year: 1996 ident: 10.1016/j.chaos.2023.113809_b29 article-title: Phase synchronization of chaotic oscillators publication-title: Phys Rev Lett doi: 10.1103/PhysRevLett.76.1804 – volume: 438 start-page: 343 year: 2006 ident: 10.1016/j.chaos.2023.113809_b5 article-title: Chaos-based communications at high bit rates using commercial fibre-optic links publication-title: Nature doi: 10.1038/nature04275 – volume: 374 start-page: 2925 year: 2010 ident: 10.1016/j.chaos.2023.113809_b8 article-title: Generalized synchronization of chaos for secure communication: remarkable stability to noise publication-title: Phys Lett A doi: 10.1016/j.physleta.2010.05.024 – volume: 22 start-page: 27896 year: 2020 ident: 10.1016/j.chaos.2023.113809_b3 article-title: The dynamic and thermodynamic origin of dissipative chaos: chemical Lorenz system publication-title: Phys Chem Chem Phys doi: 10.1039/D0CP03580G – volume: 78 start-page: 4193 year: 1997 ident: 10.1016/j.chaos.2023.113809_b21 article-title: From phase to lag synchronization in coupled chaotic oscillators publication-title: Phys Rev Lett doi: 10.1103/PhysRevLett.78.4193 – volume: 96 year: 2021 ident: 10.1016/j.chaos.2023.113809_b20 article-title: Chaos synchronization in generalized Lorenz systems and an application to image encryption publication-title: Commun Nonlinear Sci Numer Simul doi: 10.1016/j.cnsns.2021.105708 – volume: 61 start-page: 85 year: 2015 ident: 10.1016/j.chaos.2023.113809_b66 article-title: Deep learning in neural networks: an overview publication-title: Neural Netw doi: 10.1016/j.neunet.2014.09.003 – volume: 550 start-page: 354 year: 2017 ident: 10.1016/j.chaos.2023.113809_b51 article-title: Mastering the game of go without human knowledge publication-title: Nature doi: 10.1038/nature24270 – volume: 428 year: 2021 ident: 10.1016/j.chaos.2023.113809_b64 article-title: Control and anti-control of chaos based on the moving largest Lyapunov exponent using reinforcement learning publication-title: Physica D doi: 10.1016/j.physd.2021.133068 – volume: 7 start-page: 217 year: 1996 ident: 10.1016/j.chaos.2023.113809_b70 article-title: Symbolic dynamics of the Lorenz equations publication-title: Chaos Solitons Fractals doi: 10.1016/0960-0779(95)00046-1 – volume: 23 start-page: 4909 year: 2022 ident: 10.1016/j.chaos.2023.113809_b55 article-title: Deep reinforcement learning for autonomous driving: A survey publication-title: IEEE Trans Intell Transp Syst doi: 10.1109/TITS.2021.3054625 – volume: 29 year: 2019 ident: 10.1016/j.chaos.2023.113809_b59 article-title: Zermelo’s problem: optimal point-to-point navigation in 2D turbulent flows using reinforcement learning publication-title: Chaos doi: 10.1063/1.5120370 – volume: 72 year: 2005 ident: 10.1016/j.chaos.2023.113809_b30 article-title: Phase synchronization between two essentially different chaotic systems publication-title: Phys Rev E doi: 10.1103/PhysRevE.72.016205 – volume: 101 year: 2020 ident: 10.1016/j.chaos.2023.113809_b2 article-title: Intermittent chaos in cavity optomechanics publication-title: Phys Rev A doi: 10.1103/PhysRevA.101.053851 – volume: 240 start-page: 50 year: 1998 ident: 10.1016/j.chaos.2023.113809_b6 article-title: Cryptography with chaos publication-title: Phys Lett A doi: 10.1016/S0375-9601(98)00086-3 – volume: 8 start-page: 1577 year: 1997 ident: 10.1016/j.chaos.2023.113809_b71 article-title: Variable structure control approach for controlling chaos publication-title: Chaos Solitons Fractals doi: 10.1016/S0960-0779(96)00156-7 – volume: 2021 start-page: 157 year: 2021 ident: 10.1016/j.chaos.2023.113809_b15 article-title: Hyperchaotic behaviors, optimal control, and synchronization of a nonautonomous cardiac conduction system publication-title: Adv Differential Equations doi: 10.1186/s13662-021-03320-0 – volume: 50 start-page: 1894 year: 1994 ident: 10.1016/j.chaos.2023.113809_b41 article-title: Synchronization of spatiotemporal chaotic systems by feedback control publication-title: Phys Rev E doi: 10.1103/PhysRevE.50.1894 – ident: 10.1016/j.chaos.2023.113809_b69 – volume: 38 start-page: 156 year: 2008 ident: 10.1016/j.chaos.2023.113809_b49 article-title: A comprehensive survey of multiagent reinforcement learning publication-title: IEEE Trans Syst Man Cybern C doi: 10.1109/TSMCC.2007.913919 – volume: 125 start-page: 174 year: 2020 ident: 10.1016/j.chaos.2023.113809_b10 article-title: Chaos in fractional-order discrete neural networks with application to image encryption publication-title: Neural Netw doi: 10.1016/j.neunet.2020.02.008 – volume: 11 start-page: 1317 year: 2022 ident: 10.1016/j.chaos.2023.113809_b1 article-title: Cancer and chaos and the complex network model of a multicellular organism publication-title: Biology-Basel doi: 10.3390/biology11091317 – volume: 12 start-page: 671 year: 2002 ident: 10.1016/j.chaos.2023.113809_b72 article-title: Mechanical models of Chua’s circuit publication-title: Int J Bifurcation Chaos doi: 10.1142/S0218127402004668 – volume: 64 start-page: 1196 year: 1990 ident: 10.1016/j.chaos.2023.113809_b16 article-title: Controlling chaos publication-title: Phys Rev Lett doi: 10.1103/PhysRevLett.64.1196 – volume: 475 start-page: 2231 year: 2019 ident: 10.1016/j.chaos.2023.113809_b63 article-title: Control of chaotic systems by deep reinforcement learning publication-title: Proc R Soc Lond Ser A Math Phys Eng Sci |
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| Title | A deep reinforcement learning method to control chaos synchronization between two identical chaotic systems |
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