Stability of synchronized dynamics and pattern formation in coupled systems: Review of some recent results
In arbitrarily coupled dynamical systems (maps or ordinary differential equations), the stability of synchronized states (including equilibrium point, periodic orbit or chaotic attractor) and the formation of patterns from loss of stability of the synchronized states are two problems of current rese...
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| Veröffentlicht in: | Communications in nonlinear science & numerical simulation Jg. 11; H. 8; S. 934 - 960 |
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| Sprache: | Englisch |
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01.12.2006
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| ISSN: | 1007-5704, 1878-7274 |
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| Abstract | In arbitrarily coupled dynamical systems (maps or ordinary differential equations), the stability of synchronized states (including equilibrium point, periodic orbit or chaotic attractor) and the formation of patterns from loss of stability of the synchronized states are two problems of current research interest. These two problems are often treated separately in the literature. Here, we present a unified framework in which we show that the eigenvalues of the coupling matrix determine the stability of the synchronized state, while the eigenvectors correspond to patterns emerging from desynchronization. Based on this simple framework three results are derived: First, general approaches are developed that yield constraints directly on the coupling strengths which ensure the stability of synchronized dynamics. Second, when the synchronized state becomes unstable spatial patterns can be selectively realized by varying the coupling strengths. Distinct temporal evolution of the spatial pattern can be obtained depending on the bifurcating synchronized state. Third, given a desired spatiotemporal pattern, one is able to design coupling schemes which give rise to that pattern as the coupled system evolves. Systems with specific coupling schemes are used as examples to illustrate the general methods. |
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| AbstractList | In arbitrarily coupled dynamical systems (maps or ordinary differential equations), the stability of synchronized states (including equilibrium point, periodic orbit or chaotic attractor) and the formation of patterns from loss of stability of the synchronized states are two problems of current research interest. These two problems are often treated separately in the literature. Here, we present a unified framework in which we show that the eigenvalues of the coupling matrix determine the stability of the synchronized state, while the eigenvectors correspond to patterns emerging from desynchronization. Based on this simple framework three results are derived: First, general approaches are developed that yield constraints directly on the coupling strengths which ensure the stability of synchronized dynamics. Second, when the synchronized state becomes unstable spatial patterns can be selectively realized by varying the coupling strengths. Distinct temporal evolution of the spatial pattern can be obtained depending on the bifurcating synchronized state. Third, given a desired spatiotemporal pattern, one is able to design coupling schemes which give rise to that pattern as the coupled system evolves. Systems with specific coupling schemes are used as examples to illustrate the general methods. |
| Author | Rangarajan, Govindan Ding, Mingzhou Chen, Yonghong |
| Author_xml | – sequence: 1 givenname: Yonghong surname: Chen fullname: Chen, Yonghong email: ychen@bme.ufl.edu organization: Department of Biomedical Engineering, University of Florida, 120 BME Building/P.O. Box 116131, Gainesville, FL 32611, USA – sequence: 2 givenname: Govindan surname: Rangarajan fullname: Rangarajan, Govindan email: rangaraj@math.iisc.ernet.in organization: Department of Mathematics and Centre for Theoretical Studies, Indian Institute of Science, Bangalore 560 012, India – sequence: 3 givenname: Mingzhou surname: Ding fullname: Ding, Mingzhou email: ding@bme.ufl.edu organization: Department of Biomedical Engineering, University of Florida, 120 BME Building/P.O. Box 116131, Gainesville, FL 32611, USA |
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| Cites_doi | 10.1103/PhysRevLett.76.1816 10.1103/PhysRevLett.80.2109 10.1016/S0375-9601(03)00447-X 10.1142/S0218127497001898 10.1103/PhysRevE.63.067201 10.1103/PhysRevLett.84.3049 10.1016/S0375-9601(02)00051-8 10.1103/PhysRevA.36.5820 10.1103/PhysRevLett.72.2009 10.1016/0375-9601(94)90114-7 10.1103/PhysRevE.61.5080 10.1103/PhysRevE.58.347 10.1016/S0893-6080(03)00136-9 10.1103/PhysRevE.62.6332 10.1143/PTP.69.32 10.1142/S0218127494000691 10.1103/PhysRevE.50.1874 10.1103/PhysRevA.49.1301 10.1098/rstb.1952.0012 10.1016/0167-2789(90)90089-8 10.1103/PhysRevLett.77.1751 10.1103/PhysRevE.56.4009 10.1016/0167-2789(86)90149-1 10.1007/BF00200803 10.1103/PhysRevE.65.016201 10.1142/S0218127497000431 10.1162/08997660152469350 10.1016/0375-9601(84)90388-8 10.1109/81.404047 10.1142/S0129065796000385 10.1016/0030-4018(93)90078-J 10.1103/PhysRevLett.65.1575 10.1103/PhysRevE.67.026209 10.1103/PhysRevLett.68.718 10.1103/PhysRevLett.78.4189 10.1103/PhysRevE.58.4440 10.1103/PhysRevE.60.2160 10.1103/PhysRevLett.77.5361 10.1016/S0006-3495(72)86068-5 10.1162/08997660152469332 10.1103/PhysRevE.62.2963 10.1103/PhysRevLett.74.4185 10.1016/0893-6080(89)90018-X 10.1016/S0167-2789(98)00300-5 10.1016/0375-9601(94)90947-4 10.1103/PhysRevE.63.036216 10.1088/0951-7715/1/4/001 10.1103/PhysRevE.54.2489 10.1016/S0375-9601(99)00417-X 10.1143/PTP.74.918 10.1103/PhysRevLett.70.279 10.1063/1.1412576 |
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| Keywords | Coupled dynamical systems Chaotic synchronization Generalized Turing patterns 07.05.Mh 05.45.Xt 89.75.Kd |
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| References | Golub, Van Loan (bib18) 1996 Heagy, Pecora, Carroll (bib21) 1994; 50 Zhu, Chen (bib56) 2001; 63 Baird (bib1) 1990; 42 Gantmacher (bib15) 1964 Jost, Joy (bib27) 2002; 65 Fink, Johnson, Carroll, Mar, Pecora (bib11) 2000; 61 Brown, Rulkov (bib5) 1997; 78 Kocarev, Parlitz (bib29) 1996; 76 Ding, Yang (bib8) 1996; 54 Pasemann (bib38) 1999; 128 Rangarajan, Chen, Ding (bib43) 2003; 310 Hansel (bib20) 1996; 7 Rulkov, Sushchik (bib46) 1997; 7 Bresloff (bib4) 1999; 60 Roy, Thornburg (bib45) 1994; 72 Fujisaka, Yamada (bib13) 1983; 69 Hirsch, Smale (bib23) 1974 Li, Hopfield (bib30) 1989; 61 Wersing, Beyn, Ritter (bib50) 2001; 13 Turing (bib48) 1952; 237 Venkataramani (bib59) 1996; 77 Fujisaka, Yamada (bib14) 1985; 74 Murray (bib35) 1993 Glendinning (bib17) 1999; 259 Wu, Chua (bib53) 1994; 4 Hirsch (bib24) 1989; 2 Venkataramani (bib60) 1996; 54 Rangarajan, Ding (bib42) 2002; 296 Freeman (bib12) 1975 Filatrella, Straughn, Barbara (bib10) 2001; 90 Li, Erneux (bib31) 1993; 99 Munuzuri, Chua (bib34) 1997; 7 Rojas (bib44) 1996 Ashwin, Buescu, Stewart (bib58) 1994; 193 Gauthier, Bienfang (bib16) 1996; 77 Ding, Yang (bib9) 1997; 56 Truccolo, Rangarjan, Chen, Ding (bib47) 2004; 16 Zhan, Hu, Yang (bib55) 2000; 62 Winful, Rahman (bib52) 1990; 65 Otsuka, Kawai, Hwong, Ko, Chern (bib37) 2000; 84 Bunimovich, Sinai (bib6) 1988; 1 Horn, Johnson (bib25) 1985 Wilson, Cowan (bib51) 1972; 12 Belykh, Belykh, Hasler (bib2) 2000; 62 Li (bib33) 2001; 13 Waller, Kapral (bib49) 1984; 105 Kaneko (bib28) 1986; 23 Pecora, Carroll (bib40) 1998; 80 Belykh, Belykh, Mosekilde (bib3) 2001; 63 Platt, Spiegel, Tresser (bib41) 1993; 70 Li, Erneux (bib32) 1994; 49 Wu, Chua (bib54) 1995; 42 Ott, Sommerer (bib57) 1994; 188 Hu, Yang, Liu (bib26) 1998; 58 Hansel, Sompolinsky (bib19) 1992; 68 Chen, Rangarajan, Ding (bib7) 2003; 67 Heagy, Pecora, Carroll (bib22) 1995; 74 Oppo, Kapral (bib36) 1987; 36 Pecora (bib39) 1998; 58 Brown (10.1016/j.cnsns.2005.01.011_bib5) 1997; 78 Baird (10.1016/j.cnsns.2005.01.011_bib1) 1990; 42 Kaneko (10.1016/j.cnsns.2005.01.011_bib28) 1986; 23 Wilson (10.1016/j.cnsns.2005.01.011_bib51) 1972; 12 Li (10.1016/j.cnsns.2005.01.011_bib31) 1993; 99 Venkataramani (10.1016/j.cnsns.2005.01.011_bib59) 1996; 77 Heagy (10.1016/j.cnsns.2005.01.011_bib21) 1994; 50 Belykh (10.1016/j.cnsns.2005.01.011_bib2) 2000; 62 Roy (10.1016/j.cnsns.2005.01.011_bib45) 1994; 72 Golub (10.1016/j.cnsns.2005.01.011_bib18) 1996 Hansel (10.1016/j.cnsns.2005.01.011_bib20) 1996; 7 Pecora (10.1016/j.cnsns.2005.01.011_bib39) 1998; 58 Wersing (10.1016/j.cnsns.2005.01.011_bib50) 2001; 13 Gauthier (10.1016/j.cnsns.2005.01.011_bib16) 1996; 77 Jost (10.1016/j.cnsns.2005.01.011_bib27) 2002; 65 Ding (10.1016/j.cnsns.2005.01.011_bib9) 1997; 56 Hu (10.1016/j.cnsns.2005.01.011_bib26) 1998; 58 Li (10.1016/j.cnsns.2005.01.011_bib33) 2001; 13 Kocarev (10.1016/j.cnsns.2005.01.011_bib29) 1996; 76 Rangarajan (10.1016/j.cnsns.2005.01.011_bib43) 2003; 310 Fujisaka (10.1016/j.cnsns.2005.01.011_bib13) 1983; 69 Turing (10.1016/j.cnsns.2005.01.011_bib48) 1952; 237 Zhu (10.1016/j.cnsns.2005.01.011_bib56) 2001; 63 Venkataramani (10.1016/j.cnsns.2005.01.011_bib60) 1996; 54 Ott (10.1016/j.cnsns.2005.01.011_bib57) 1994; 188 Glendinning (10.1016/j.cnsns.2005.01.011_bib17) 1999; 259 Zhan (10.1016/j.cnsns.2005.01.011_bib55) 2000; 62 Platt (10.1016/j.cnsns.2005.01.011_bib41) 1993; 70 Ashwin (10.1016/j.cnsns.2005.01.011_bib58) 1994; 193 Horn (10.1016/j.cnsns.2005.01.011_bib25) 1985 Heagy (10.1016/j.cnsns.2005.01.011_bib22) 1995; 74 Li (10.1016/j.cnsns.2005.01.011_bib30) 1989; 61 Fujisaka (10.1016/j.cnsns.2005.01.011_bib14) 1985; 74 Ding (10.1016/j.cnsns.2005.01.011_bib8) 1996; 54 Bunimovich (10.1016/j.cnsns.2005.01.011_bib6) 1988; 1 Hirsch (10.1016/j.cnsns.2005.01.011_bib23) 1974 Li (10.1016/j.cnsns.2005.01.011_bib32) 1994; 49 Murray (10.1016/j.cnsns.2005.01.011_bib35) 1993 Otsuka (10.1016/j.cnsns.2005.01.011_bib37) 2000; 84 Hansel (10.1016/j.cnsns.2005.01.011_bib19) 1992; 68 Belykh (10.1016/j.cnsns.2005.01.011_bib3) 2001; 63 Wu (10.1016/j.cnsns.2005.01.011_bib53) 1994; 4 Chen (10.1016/j.cnsns.2005.01.011_bib7) 2003; 67 Filatrella (10.1016/j.cnsns.2005.01.011_bib10) 2001; 90 Munuzuri (10.1016/j.cnsns.2005.01.011_bib34) 1997; 7 Freeman (10.1016/j.cnsns.2005.01.011_bib12) 1975 Hirsch (10.1016/j.cnsns.2005.01.011_bib24) 1989; 2 Winful (10.1016/j.cnsns.2005.01.011_bib52) 1990; 65 Waller (10.1016/j.cnsns.2005.01.011_bib49) 1984; 105 Wu (10.1016/j.cnsns.2005.01.011_bib54) 1995; 42 Bresloff (10.1016/j.cnsns.2005.01.011_bib4) 1999; 60 Fink (10.1016/j.cnsns.2005.01.011_bib11) 2000; 61 Rojas (10.1016/j.cnsns.2005.01.011_bib44) 1996 Pasemann (10.1016/j.cnsns.2005.01.011_bib38) 1999; 128 Truccolo (10.1016/j.cnsns.2005.01.011_bib47) 2004; 16 Rangarajan (10.1016/j.cnsns.2005.01.011_bib42) 2002; 296 Rulkov (10.1016/j.cnsns.2005.01.011_bib46) 1997; 7 Oppo (10.1016/j.cnsns.2005.01.011_bib36) 1987; 36 Gantmacher (10.1016/j.cnsns.2005.01.011_bib15) 1964 Pecora (10.1016/j.cnsns.2005.01.011_bib40) 1998; 80 |
| References_xml | – volume: 42 start-page: 430 year: 1995 end-page: 447 ident: bib54 article-title: Synchronization in an array of linearly coupled dynamical systems publication-title: IEEE Trans Circuits Syst I – volume: 90 start-page: 5675 year: 2001 end-page: 5679 ident: bib10 article-title: Emission of radiation from square arrays of stacked Josephson junctions publication-title: J Appl Phys – volume: 60 start-page: 2160 year: 1999 end-page: 2170 ident: bib4 article-title: Mean-field theory of globally coupled integrate-and-fire neural oscillators with dynamic synapses publication-title: Phys Rev E – volume: 128 start-page: 236 year: 1999 end-page: 249 ident: bib38 article-title: Synchronized chaos and other coherent states for two coupled neurons publication-title: Physica D – volume: 65 start-page: 016201 year: 2002 ident: bib27 article-title: Spectral properties and synchronization in coupled map lattices publication-title: Phys Rev E – volume: 296 start-page: 204 year: 2002 end-page: 209 ident: bib42 article-title: Stability of synchronized chaos in coupled dynamical systems publication-title: Phys Lett A – volume: 58 start-page: 4440 year: 1998 end-page: 4453 ident: bib26 article-title: Instability and controllability of linearly coupled oscillators: eigenvalue analysis publication-title: Phys Rev E – volume: 61 start-page: 379 year: 1989 end-page: 392 ident: bib30 article-title: Modeling the olfactory bulb and its neural oscillatory processings publication-title: Biol Cybernet – volume: 23 start-page: 436 year: 1986 end-page: 447 ident: bib28 article-title: Lyapunov analysis and information flow in coupled map lattices publication-title: Physica D – year: 1975 ident: bib12 article-title: Mass action in the nervous system – volume: 72 start-page: 2009 year: 1994 end-page: 2012 ident: bib45 article-title: Experimental synchronization of chaotic lasers publication-title: Phys Rev Lett – volume: 50 start-page: 1874 year: 1994 end-page: 1885 ident: bib21 article-title: Synchronous chaos in coupled oscillator systems publication-title: Phys Rev E – volume: 193 start-page: 126 year: 1994 end-page: 139 ident: bib58 article-title: Bubbling of attractors and synchronisation of chaotic oscillators publication-title: Phys Lett A – volume: 1 start-page: 491 year: 1988 end-page: 516 ident: bib6 article-title: Spacetime chaos in coupled map lattices publication-title: Nonlinearity – volume: 78 start-page: 4189 year: 1997 end-page: 4192 ident: bib5 article-title: Designing a coupling that guarantees synchronization between identical chaotic systems publication-title: Phys Rev Lett – year: 1974 ident: bib23 article-title: Differential equations, dynamical systems, and linear algebra – volume: 63 start-page: 036216 year: 2001 ident: bib3 article-title: Cluster synchronization modes in an ensemble of coupled chaotic oscillators publication-title: Phys Rev E – volume: 2 start-page: 331 year: 1989 end-page: 349 ident: bib24 article-title: Convergent activation dynamics in continuous time networks publication-title: Neural Networks – volume: 62 start-page: 6332 year: 2000 end-page: 6345 ident: bib2 article-title: Hierarchy and stability of partially synchronous oscillations of diffusively coupled dynamical systems publication-title: Phys Rev E – volume: 7 start-page: 2807 year: 1997 end-page: 2825 ident: bib34 article-title: Stationary structures in a discrete bistable reaction–diffusion system publication-title: Int J Bifurc Chaos – volume: 70 start-page: 279 year: 1993 end-page: 282 ident: bib41 article-title: On–off intermittency: a mechanism for bursting publication-title: Phys Rev Lett – volume: 105 start-page: 163 year: 1984 end-page: 168 ident: bib49 article-title: Synchronization and chaos in coupled nonlinear oscillators publication-title: Phys Lett A – volume: 13 start-page: 1811 year: 2001 end-page: 1825 ident: bib50 article-title: Dynamical stability conditions for recurrent neural networks with unsaturating piecewise linear transfer functions publication-title: Neural Comput – volume: 80 start-page: 2109 year: 1998 end-page: 2112 ident: bib40 article-title: Master stability functions for synchronized coupled systems publication-title: Phys Rev Lett – volume: 62 start-page: 2963 year: 2000 end-page: 2966 ident: bib55 article-title: Synchronization of chaos in coupled systems publication-title: Phys Rev E – volume: 56 start-page: 4009 year: 1997 end-page: 4016 ident: bib9 article-title: Stability of synchronous chaos and on–off intermittency in coupled map lattices publication-title: Phys Rev E – volume: 76 start-page: 1816 year: 1996 end-page: 1819 ident: bib29 article-title: Generalized synchronization, predictability, and equivalence of unidirectionally coupled dynamical systems publication-title: Phys Rev Lett – volume: 74 start-page: 918 year: 1985 end-page: 921 ident: bib14 article-title: A new intermittency in coupled dynamical systems publication-title: Prog Theor Phys – volume: 84 start-page: 3049 year: 2000 end-page: 3052 ident: bib37 article-title: Synchronization of mutually coupled self-mixing modulated lasers publication-title: Phys Rev Lett – volume: 77 start-page: 1751 year: 1996 end-page: 1754 ident: bib16 article-title: Intermittent loss of synchronization in coupled chaotic oscillators: toward a new criterion for high-quality synchronization publication-title: Phys Rev Lett – year: 1996 ident: bib44 article-title: Neural networks—a systematic introduction – year: 1985 ident: bib25 article-title: Matrix analysis – volume: 77 start-page: 5361 year: 1996 end-page: 5364 ident: bib59 article-title: Transitions to bubbling of chaotic systems publication-title: Phys Rev Lett – volume: 7 start-page: 625 year: 1997 end-page: 643 ident: bib46 article-title: Robustness of synchronized chaotic oscillations publication-title: Int J Bifurc Chaos – volume: 99 start-page: 196 year: 1993 end-page: 200 ident: bib31 article-title: Stability conditions for coupled lasers—series coupling versus parallel coupling publication-title: Opt Commun – volume: 42 start-page: 365 year: 1990 end-page: 384 ident: bib1 article-title: Bifurcation and category learning in network models of oscillating cortex publication-title: Physica D – volume: 188 start-page: 39 year: 1994 end-page: 47 ident: bib57 article-title: Blowout bifurcations: the occurrence of riddled basins and on–off intermittency publication-title: Phys Lett A – volume: 63 start-page: 067201 year: 2001 ident: bib56 article-title: Controlling spatiotemporal chaos in coupled map lattices publication-title: Phys Rev E – volume: 67 start-page: 026209 year: 2003 ident: bib7 article-title: General stability analysis of synchronized dynamics in coupled systems publication-title: Phys Rev E – volume: 13 start-page: 1749 year: 2001 end-page: 1780 ident: bib33 article-title: Computational design and nonlinear dynamics of a recurrent network model of the primary visual cortex publication-title: Neural Comput – volume: 310 start-page: 415 year: 2003 end-page: 422 ident: bib43 article-title: Generalized Turing patterns and their selective realization in spatiotemporal systems publication-title: Phys Lett A – volume: 54 start-page: 2489 year: 1996 end-page: 2494 ident: bib8 article-title: Observation of intermingled basins in coupled oscillators exhibiting synchronized chaos publication-title: Phys Rev E – volume: 68 start-page: 718 year: 1992 end-page: 721 ident: bib19 article-title: Synchronization and computation in a chaotic neural network publication-title: Phys Rev Lett – volume: 58 start-page: 347 year: 1998 end-page: 360 ident: bib39 article-title: Synchronization conditions and desynchronizing patterns in coupled limit-cycle and chaotic systems publication-title: Phys Rev E – volume: 49 start-page: 1301 year: 1994 end-page: 1312 ident: bib32 article-title: Bifurcation to standing and traveling waves in large arrays of coupled lasers publication-title: Phys Rev A – year: 1993 ident: bib35 article-title: Mathematical biology – volume: 4 start-page: 979 year: 1994 end-page: 998 ident: bib53 article-title: A unified framework for synchronization and control of dynamical systems publication-title: Int J Bifurc Chaos – volume: 54 start-page: 1346 year: 1996 end-page: 1349 ident: bib60 article-title: Classical diffusion on Eden trees publication-title: Phys Rev Lett – year: 1964 ident: bib15 article-title: Theory of matrices – volume: 7 start-page: 403 year: 1996 end-page: 415 ident: bib20 article-title: Synchronized chaos in local cortical circuits publication-title: Int J Neural Syst – volume: 65 start-page: 1575 year: 1990 end-page: 1578 ident: bib52 article-title: Synchronized chaos and spatiotemporal chaos in arrays of coupled lasers publication-title: Phys Rev Lett – volume: 74 start-page: 2188 year: 1995 end-page: 4185 ident: bib22 article-title: Short wavelength bifurcations and size instabilities in coupled oscillator systems publication-title: Phys Rev Lett – volume: 259 start-page: 129 year: 1999 end-page: 134 ident: bib17 article-title: The stability boundary of synchronized states in globally coupled dynamical systems publication-title: Phys Lett A – year: 1996 ident: bib18 article-title: Matrix computations – volume: 36 start-page: 5820 year: 1987 end-page: 5831 ident: bib36 article-title: Domain growth and nucleation in a discrete bistable system publication-title: Phys Rev A – volume: 16 start-page: 1453 year: 2004 end-page: 1460 ident: bib47 article-title: Analyzing stability of equilibrium points in neural networks: a general approach publication-title: Neural Networks – volume: 61 start-page: 5080 year: 2000 end-page: 5090 ident: bib11 article-title: Three coupled oscillators as a universal probe of synchronization stability in coupled oscillator arrays publication-title: Phys Rev E – volume: 237 start-page: 37 year: 1952 end-page: 72 ident: bib48 article-title: The chemical basis of morphogenesis publication-title: Phil Trans Roy Soc B – volume: 12 start-page: 1 year: 1972 end-page: 24 ident: bib51 article-title: Excitatory and inhibitory interactions in localized populations of model neurons publication-title: Biophys J – volume: 69 start-page: 32 year: 1983 end-page: 47 ident: bib13 article-title: Stability theory of synchronized motion in coupled oscillator systems publication-title: Prog Theor Phys – volume: 76 start-page: 1816 issue: 11 year: 1996 ident: 10.1016/j.cnsns.2005.01.011_bib29 article-title: Generalized synchronization, predictability, and equivalence of unidirectionally coupled dynamical systems publication-title: Phys Rev Lett doi: 10.1103/PhysRevLett.76.1816 – volume: 80 start-page: 2109 issue: 10 year: 1998 ident: 10.1016/j.cnsns.2005.01.011_bib40 article-title: Master stability functions for synchronized coupled systems publication-title: Phys Rev Lett doi: 10.1103/PhysRevLett.80.2109 – volume: 54 start-page: 1346 year: 1996 ident: 10.1016/j.cnsns.2005.01.011_bib60 article-title: Classical diffusion on Eden trees publication-title: Phys Rev Lett – volume: 310 start-page: 415 year: 2003 ident: 10.1016/j.cnsns.2005.01.011_bib43 article-title: Generalized Turing patterns and their selective realization in spatiotemporal systems publication-title: Phys Lett A doi: 10.1016/S0375-9601(03)00447-X – volume: 7 start-page: 2807 issue: 12 year: 1997 ident: 10.1016/j.cnsns.2005.01.011_bib34 article-title: Stationary structures in a discrete bistable reaction–diffusion system publication-title: Int J Bifurc Chaos doi: 10.1142/S0218127497001898 – volume: 63 start-page: 067201 year: 2001 ident: 10.1016/j.cnsns.2005.01.011_bib56 article-title: Controlling spatiotemporal chaos in coupled map lattices publication-title: Phys Rev E doi: 10.1103/PhysRevE.63.067201 – volume: 84 start-page: 3049 issue: 14 year: 2000 ident: 10.1016/j.cnsns.2005.01.011_bib37 article-title: Synchronization of mutually coupled self-mixing modulated lasers publication-title: Phys Rev Lett doi: 10.1103/PhysRevLett.84.3049 – volume: 296 start-page: 204 issue: 4–5 year: 2002 ident: 10.1016/j.cnsns.2005.01.011_bib42 article-title: Stability of synchronized chaos in coupled dynamical systems publication-title: Phys Lett A doi: 10.1016/S0375-9601(02)00051-8 – year: 1996 ident: 10.1016/j.cnsns.2005.01.011_bib44 – volume: 36 start-page: 5820 issue: 12 year: 1987 ident: 10.1016/j.cnsns.2005.01.011_bib36 article-title: Domain growth and nucleation in a discrete bistable system publication-title: Phys Rev A doi: 10.1103/PhysRevA.36.5820 – year: 1974 ident: 10.1016/j.cnsns.2005.01.011_bib23 – volume: 72 start-page: 2009 issue: 13 year: 1994 ident: 10.1016/j.cnsns.2005.01.011_bib45 article-title: Experimental synchronization of chaotic lasers publication-title: Phys Rev Lett doi: 10.1103/PhysRevLett.72.2009 – volume: 188 start-page: 39 year: 1994 ident: 10.1016/j.cnsns.2005.01.011_bib57 article-title: Blowout bifurcations: the occurrence of riddled basins and on–off intermittency publication-title: Phys Lett A doi: 10.1016/0375-9601(94)90114-7 – year: 1996 ident: 10.1016/j.cnsns.2005.01.011_bib18 – volume: 61 start-page: 5080 issue: 5 year: 2000 ident: 10.1016/j.cnsns.2005.01.011_bib11 article-title: Three coupled oscillators as a universal probe of synchronization stability in coupled oscillator arrays publication-title: Phys Rev E doi: 10.1103/PhysRevE.61.5080 – volume: 58 start-page: 347 issue: 1 year: 1998 ident: 10.1016/j.cnsns.2005.01.011_bib39 article-title: Synchronization conditions and desynchronizing patterns in coupled limit-cycle and chaotic systems publication-title: Phys Rev E doi: 10.1103/PhysRevE.58.347 – volume: 16 start-page: 1453 year: 2004 ident: 10.1016/j.cnsns.2005.01.011_bib47 article-title: Analyzing stability of equilibrium points in neural networks: a general approach publication-title: Neural Networks doi: 10.1016/S0893-6080(03)00136-9 – volume: 62 start-page: 6332 issue: 5 year: 2000 ident: 10.1016/j.cnsns.2005.01.011_bib2 article-title: Hierarchy and stability of partially synchronous oscillations of diffusively coupled dynamical systems publication-title: Phys Rev E doi: 10.1103/PhysRevE.62.6332 – volume: 69 start-page: 32 issue: 1 year: 1983 ident: 10.1016/j.cnsns.2005.01.011_bib13 article-title: Stability theory of synchronized motion in coupled oscillator systems publication-title: Prog Theor Phys doi: 10.1143/PTP.69.32 – year: 1985 ident: 10.1016/j.cnsns.2005.01.011_bib25 – volume: 4 start-page: 979 issue: 4 year: 1994 ident: 10.1016/j.cnsns.2005.01.011_bib53 article-title: A unified framework for synchronization and control of dynamical systems publication-title: Int J Bifurc Chaos doi: 10.1142/S0218127494000691 – volume: 50 start-page: 1874 issue: 3 year: 1994 ident: 10.1016/j.cnsns.2005.01.011_bib21 article-title: Synchronous chaos in coupled oscillator systems publication-title: Phys Rev E doi: 10.1103/PhysRevE.50.1874 – volume: 49 start-page: 1301 issue: 2 year: 1994 ident: 10.1016/j.cnsns.2005.01.011_bib32 article-title: Bifurcation to standing and traveling waves in large arrays of coupled lasers publication-title: Phys Rev A doi: 10.1103/PhysRevA.49.1301 – volume: 237 start-page: 37 issue: 64 year: 1952 ident: 10.1016/j.cnsns.2005.01.011_bib48 article-title: The chemical basis of morphogenesis publication-title: Phil Trans Roy Soc B doi: 10.1098/rstb.1952.0012 – volume: 42 start-page: 365 issue: 1–3 year: 1990 ident: 10.1016/j.cnsns.2005.01.011_bib1 article-title: Bifurcation and category learning in network models of oscillating cortex publication-title: Physica D doi: 10.1016/0167-2789(90)90089-8 – volume: 77 start-page: 1751 issue: 9 year: 1996 ident: 10.1016/j.cnsns.2005.01.011_bib16 article-title: Intermittent loss of synchronization in coupled chaotic oscillators: toward a new criterion for high-quality synchronization publication-title: Phys Rev Lett doi: 10.1103/PhysRevLett.77.1751 – volume: 56 start-page: 4009 issue: 4 year: 1997 ident: 10.1016/j.cnsns.2005.01.011_bib9 article-title: Stability of synchronous chaos and on–off intermittency in coupled map lattices publication-title: Phys Rev E doi: 10.1103/PhysRevE.56.4009 – volume: 23 start-page: 436 issue: 1–3 year: 1986 ident: 10.1016/j.cnsns.2005.01.011_bib28 article-title: Lyapunov analysis and information flow in coupled map lattices publication-title: Physica D doi: 10.1016/0167-2789(86)90149-1 – volume: 61 start-page: 379 issue: 5 year: 1989 ident: 10.1016/j.cnsns.2005.01.011_bib30 article-title: Modeling the olfactory bulb and its neural oscillatory processings publication-title: Biol Cybernet doi: 10.1007/BF00200803 – volume: 65 start-page: 016201 year: 2002 ident: 10.1016/j.cnsns.2005.01.011_bib27 article-title: Spectral properties and synchronization in coupled map lattices publication-title: Phys Rev E doi: 10.1103/PhysRevE.65.016201 – volume: 7 start-page: 625 issue: 3 year: 1997 ident: 10.1016/j.cnsns.2005.01.011_bib46 article-title: Robustness of synchronized chaotic oscillations publication-title: Int J Bifurc Chaos doi: 10.1142/S0218127497000431 – volume: 13 start-page: 1811 issue: 8 year: 2001 ident: 10.1016/j.cnsns.2005.01.011_bib50 article-title: Dynamical stability conditions for recurrent neural networks with unsaturating piecewise linear transfer functions publication-title: Neural Comput doi: 10.1162/08997660152469350 – volume: 105 start-page: 163 issue: 4–5 year: 1984 ident: 10.1016/j.cnsns.2005.01.011_bib49 article-title: Synchronization and chaos in coupled nonlinear oscillators publication-title: Phys Lett A doi: 10.1016/0375-9601(84)90388-8 – volume: 42 start-page: 430 issue: 8 year: 1995 ident: 10.1016/j.cnsns.2005.01.011_bib54 article-title: Synchronization in an array of linearly coupled dynamical systems publication-title: IEEE Trans Circuits Syst I doi: 10.1109/81.404047 – volume: 7 start-page: 403 issue: 4 year: 1996 ident: 10.1016/j.cnsns.2005.01.011_bib20 article-title: Synchronized chaos in local cortical circuits publication-title: Int J Neural Syst doi: 10.1142/S0129065796000385 – year: 1993 ident: 10.1016/j.cnsns.2005.01.011_bib35 – volume: 99 start-page: 196 issue: 3–4 year: 1993 ident: 10.1016/j.cnsns.2005.01.011_bib31 article-title: Stability conditions for coupled lasers—series coupling versus parallel coupling publication-title: Opt Commun doi: 10.1016/0030-4018(93)90078-J – volume: 65 start-page: 1575 issue: 13 year: 1990 ident: 10.1016/j.cnsns.2005.01.011_bib52 article-title: Synchronized chaos and spatiotemporal chaos in arrays of coupled lasers publication-title: Phys Rev Lett doi: 10.1103/PhysRevLett.65.1575 – volume: 67 start-page: 026209 year: 2003 ident: 10.1016/j.cnsns.2005.01.011_bib7 article-title: General stability analysis of synchronized dynamics in coupled systems publication-title: Phys Rev E doi: 10.1103/PhysRevE.67.026209 – volume: 68 start-page: 718 issue: 5 year: 1992 ident: 10.1016/j.cnsns.2005.01.011_bib19 article-title: Synchronization and computation in a chaotic neural network publication-title: Phys Rev Lett doi: 10.1103/PhysRevLett.68.718 – volume: 78 start-page: 4189 issue: 22 year: 1997 ident: 10.1016/j.cnsns.2005.01.011_bib5 article-title: Designing a coupling that guarantees synchronization between identical chaotic systems publication-title: Phys Rev Lett doi: 10.1103/PhysRevLett.78.4189 – volume: 58 start-page: 4440 issue: 4 year: 1998 ident: 10.1016/j.cnsns.2005.01.011_bib26 article-title: Instability and controllability of linearly coupled oscillators: eigenvalue analysis publication-title: Phys Rev E doi: 10.1103/PhysRevE.58.4440 – volume: 60 start-page: 2160 issue: 2 year: 1999 ident: 10.1016/j.cnsns.2005.01.011_bib4 article-title: Mean-field theory of globally coupled integrate-and-fire neural oscillators with dynamic synapses publication-title: Phys Rev E doi: 10.1103/PhysRevE.60.2160 – volume: 77 start-page: 5361 year: 1996 ident: 10.1016/j.cnsns.2005.01.011_bib59 article-title: Transitions to bubbling of chaotic systems publication-title: Phys Rev Lett doi: 10.1103/PhysRevLett.77.5361 – year: 1975 ident: 10.1016/j.cnsns.2005.01.011_bib12 – volume: 12 start-page: 1 issue: 1 year: 1972 ident: 10.1016/j.cnsns.2005.01.011_bib51 article-title: Excitatory and inhibitory interactions in localized populations of model neurons publication-title: Biophys J doi: 10.1016/S0006-3495(72)86068-5 – volume: 13 start-page: 1749 issue: 8 year: 2001 ident: 10.1016/j.cnsns.2005.01.011_bib33 article-title: Computational design and nonlinear dynamics of a recurrent network model of the primary visual cortex publication-title: Neural Comput doi: 10.1162/08997660152469332 – volume: 62 start-page: 2963 issue: 2 year: 2000 ident: 10.1016/j.cnsns.2005.01.011_bib55 article-title: Synchronization of chaos in coupled systems publication-title: Phys Rev E doi: 10.1103/PhysRevE.62.2963 – volume: 74 start-page: 2188 issue: 21 year: 1995 ident: 10.1016/j.cnsns.2005.01.011_bib22 article-title: Short wavelength bifurcations and size instabilities in coupled oscillator systems publication-title: Phys Rev Lett doi: 10.1103/PhysRevLett.74.4185 – volume: 2 start-page: 331 issue: 5 year: 1989 ident: 10.1016/j.cnsns.2005.01.011_bib24 article-title: Convergent activation dynamics in continuous time networks publication-title: Neural Networks doi: 10.1016/0893-6080(89)90018-X – volume: 128 start-page: 236 issue: 2–4 year: 1999 ident: 10.1016/j.cnsns.2005.01.011_bib38 article-title: Synchronized chaos and other coherent states for two coupled neurons publication-title: Physica D doi: 10.1016/S0167-2789(98)00300-5 – year: 1964 ident: 10.1016/j.cnsns.2005.01.011_bib15 – volume: 193 start-page: 126 year: 1994 ident: 10.1016/j.cnsns.2005.01.011_bib58 article-title: Bubbling of attractors and synchronisation of chaotic oscillators publication-title: Phys Lett A doi: 10.1016/0375-9601(94)90947-4 – volume: 63 start-page: 036216 year: 2001 ident: 10.1016/j.cnsns.2005.01.011_bib3 article-title: Cluster synchronization modes in an ensemble of coupled chaotic oscillators publication-title: Phys Rev E doi: 10.1103/PhysRevE.63.036216 – volume: 1 start-page: 491 issue: 4 year: 1988 ident: 10.1016/j.cnsns.2005.01.011_bib6 article-title: Spacetime chaos in coupled map lattices publication-title: Nonlinearity doi: 10.1088/0951-7715/1/4/001 – volume: 54 start-page: 2489 issue: 3 year: 1996 ident: 10.1016/j.cnsns.2005.01.011_bib8 article-title: Observation of intermingled basins in coupled oscillators exhibiting synchronized chaos publication-title: Phys Rev E doi: 10.1103/PhysRevE.54.2489 – volume: 259 start-page: 129 issue: 2 year: 1999 ident: 10.1016/j.cnsns.2005.01.011_bib17 article-title: The stability boundary of synchronized states in globally coupled dynamical systems publication-title: Phys Lett A doi: 10.1016/S0375-9601(99)00417-X – volume: 74 start-page: 918 issue: 4 year: 1985 ident: 10.1016/j.cnsns.2005.01.011_bib14 article-title: A new intermittency in coupled dynamical systems publication-title: Prog Theor Phys doi: 10.1143/PTP.74.918 – volume: 70 start-page: 279 issue: 3 year: 1993 ident: 10.1016/j.cnsns.2005.01.011_bib41 article-title: On–off intermittency: a mechanism for bursting publication-title: Phys Rev Lett doi: 10.1103/PhysRevLett.70.279 – volume: 90 start-page: 5675 issue: 11 year: 2001 ident: 10.1016/j.cnsns.2005.01.011_bib10 article-title: Emission of radiation from square arrays of stacked Josephson junctions publication-title: J Appl Phys doi: 10.1063/1.1412576 |
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