Dynamic Analysis on Reaction-diffusion Genetic Regulatory Networks with Delays
In this paper, we propose a reaction-diffusion genetic regulatory network with Neumann boundary conditions. We incorporate the diffusion factors into the delayed mathematical model of genetic networks, and with the time delays, we demonstrate the local stability and Hopf bifurcation in accordance wi...
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| Vydáno v: | Journal of physics. Conference series Ročník 2999; číslo 1; s. 12009 - 12017 |
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| Jazyk: | angličtina |
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01.04.2025
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| ISSN: | 1742-6588, 1742-6596 |
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| Abstract | In this paper, we propose a reaction-diffusion genetic regulatory network with Neumann boundary conditions. We incorporate the diffusion factors into the delayed mathematical model of genetic networks, and with the time delays, we demonstrate the local stability and Hopf bifurcation in accordance with the Hopf bifurcation theory. When the sum of the delays exceeds the critical value, a Hopf bifurcation occurs. Finally, we select the appropriate system parameters and present a numerical simulation to illustrate the theoretical analysis. |
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| AbstractList | In this paper, we propose a reaction-diffusion genetic regulatory network with Neumann boundary conditions. We incorporate the diffusion factors into the delayed mathematical model of genetic networks, and with the time delays, we demonstrate the local stability and Hopf bifurcation in accordance with the Hopf bifurcation theory. When the sum of the delays exceeds the critical value, a Hopf bifurcation occurs. Finally, we select the appropriate system parameters and present a numerical simulation to illustrate the theoretical analysis. |
| Author | Sun, Qingshan Lin, Zhi Wang, Guangwen |
| Author_xml | – sequence: 1 givenname: Qingshan surname: Sun fullname: Sun, Qingshan organization: Nanjing University of Science and Technology Zijin College School of Intelligent Control, Nanjing 210046, Jiangsu Province, China – sequence: 2 givenname: Zhi surname: Lin fullname: Lin, Zhi organization: Nanjing University of Science and Technology Zijin College School of Intelligent Control, Nanjing 210046, Jiangsu Province, China – sequence: 3 givenname: Guangwen surname: Wang fullname: Wang, Guangwen organization: Nanjing University of Science and Technology Zijin College School of Intelligent Control, Nanjing 210046, Jiangsu Province, China |
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| Cites_doi | 10.1016/j.neucom.2019.02.011 10.1109/TNNLS.2016.2618899 10.1007/s11587-023-00816-7 10.1016/j.apm.2020.08.030 10.1016/j.chaos.2021.111752 10.1007/s00034-015-0006-8 |
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| References_xml | – volume: 5110 start-page: 114 year: 2003 ident: JPCS_2999_1_012009bib7 article-title: Mesoscopic reaction-diffusion in intracellular signaling[J] publication-title: Fluct. Noise Biol. Biophys. Biomed. Syst. – volume: 338 start-page: 222 year: 2019 ident: JPCS_2999_1_012009bib6 article-title: Finite-time adaptive stability of gene regulatory networks[J] publication-title: Neurocomputing doi: 10.1016/j.neucom.2019.02.011 – start-page: 202 year: 2015 ident: JPCS_2999_1_012009bib4 article-title: Stability and bifurcation analysis of cyclic genetic regulatory networks with mixed time delays[J] – start-page: 123 year: 2017 ident: JPCS_2999_1_012009bib5 article-title: Stochastic stabilization of genetic regulatory networks[J] – volume: 29 start-page: 299 year: 2018 ident: JPCS_2999_1_012009bib11 article-title: State estimation for delayed genetic regulatory networks with reaction-diffusion terms[J] publication-title: IEEE Trans. NeuralNetw. Learn. Syst. doi: 10.1109/TNNLS.2016.2618899 – volume: 73 start-page: 137 year: 2024 ident: JPCS_2999_1_012009bib14 article-title: Excitable FitzHugh-Nagumo model with cross-diffusion: close and far-from-equilibrium coherent structures[J] publication-title: Ricerche di Matematica doi: 10.1007/s11587-023-00816-7 – start-page: 2790 year: 2011 ident: JPCS_2999_1_012009bib9 article-title: Finite-time robust stochastic stability of uncertain stochastic delayed reaction-diffusion genetic regulatory networks[J] – start-page: 1409 year: 2003 ident: JPCS_2999_1_012009bib3 article-title: Oscillatory expression of Hes1 and NF-ĸB driven by transcriptional time delays[J] – volume: 89 start-page: 1663 year: 2021 ident: JPCS_2999_1_012009bib12 article-title: Bifurcation and turing instability for apredator-prey model with nonlinear reaction cross-diffusion[J] publication-title: Appl. Math. Model. doi: 10.1016/j.apm.2020.08.030 – volume: 155 year: 2022 ident: JPCS_2999_1_012009bib13 article-title: Turing instability of periodic solutions for the Gierer-Meinhardt model with cross-diffusion[J] publication-title: Chaos Solitons and Fractals doi: 10.1016/j.chaos.2021.111752 – year: 2001 ident: JPCS_2999_1_012009bib1 – volume: 34 start-page: 3161 year: 2015 ident: JPCS_2999_1_012009bib10 article-title: Asymptotic stability criteria for genetic regulatory networks with time-varying delays and reaction-diffusion terms[J] publication-title: Circuits Syst. Signal Process doi: 10.1007/s00034-015-0006-8 – start-page: 1398 year: 2003 ident: JPCS_2999_1_012009bib2 article-title: Autoinhibition with transcriptional delay: a simple mechanism for the zebrafish somitogenesis oscillator[J] – volume: 20 start-page: 507 year: 2011 ident: JPCS_2999_1_012009bib8 article-title: Stability analysis for delayed genetic regulatory networks with reaction-diffusion terms[J] publication-title: NeuralComput. Appl. |
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| SubjectTerms | Bifurcation theory Boundary conditions Hopf bifurcation |
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| Title | Dynamic Analysis on Reaction-diffusion Genetic Regulatory Networks with Delays |
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