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Date Published: 08/11/2023
Online Published: 08/11/2023
Abstract Views: 63
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DOI: https://doi.org/10.52714/dthu.12.8.2023.1153
Issue
Vol. 12 No. 8 (2023): Natural Sciences Issue (Vietnamese)
Section
Natural Sciences Issue (Vietnamese)
How to Cite
Phan, V. L. E., & Vo, T. D. (2023). Sufficient condition for generalized synchronization in the networks of two ordinary differential equations of FitzHugh-Nagumo type with bidirectionally linear coupling. Dong Thap University Journal of Science, 12(8), 66-70. https://doi.org/10.52714/dthu.12.8.2023.1153

Sufficient condition for generalized synchronization in the networks of two ordinary differential equations of FitzHugh-Nagumo type with bidirectionally linear coupling

Van Long Em Phan1, , Tan Dat Vo2
1 Faculty of Pedagogical, An Giang University, Vietnam National University Ho Chi Minh City, Vietnam
2 Student, Faculty of Pedagogical, An Giang University, Vietnam National University Ho Chi Minh City, Vietnam

Main Article Content

Abstract

This paper studies the generalized synchronization in the network of two ordinary differential equations of FitzHugh-Nagumo type with bidirectionally linear coupling. Specifically, it examines the sufficient conditions on the coupling strength to get the generalized synchronization and simulations for checking the theoretical results.

Article Details

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This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

Keywords

generalized synchronization, ordinary differential equations of FitzHugh-Nagumo, bidirectionally linear coupling

References

Aeyels, D. (1995). Asymptotic Stability of Nonautonomous Systems by Lyapunov's Direct Method. Systems and Control Letters, 25, 273-280. http://dx.doi.org/10.1016/0167-6911(94)00088-d.
Aziz-Alaoui, M. A. (2006). Synchronization of Chaos. Encyclopedia of Mathematical Physics, Elsevier, 5, 213-226. http://dx.doi.org/10.1016/b0-12-512666-2/00105-x.
Ambrosio, B., & Aziz-Alaoui, M. A. (2012). Synchronization and control of coupled reaction-diffusion systems of the FitzHugh-Nagumo-type. Computers and Mathematics with Application, 64, 934-943. http://dx.doi.org/10.1016/j.camwa.2012.01.056.
Ambrosio, B., & Aziz-Alaoui, M. A. (2013). Synchronization and control of a network of coupled reaction-diffusion systems of generalized FitzHugh-Nagumo type. ESAIM: Proceedings and Surveys, 39, 15-24. http://dx.doi.org/10.1051/proc/201339003.
Ambrosio, B., Aziz-Alaoui, M. A. & Phan V. L. E. (2018). Global attractor of complex networks of reaction-diffusion systems of Fitzhugh-Nagumo type. American institute of mathematical sciences, 23 (9), 3787-3797. http://dx.doi.org/10.3934/dcdsb.2018077.
Braun, H.A., Wissing, H., Schäfer, K., & Hirsch, M.C. (1994). Oscillation and noise determine signal transduction in shark multimodel sensory cells. Nature, 367, 270-273. http://dx.doi.org/10.1038/367270a0.
Ermentrout, G. B., & Terman, D. H. (2009). Mathematical Foundations of Neurosciences. Springer.
Fitzhugh, R. (1960). Thresholds and plateaus in the Hodgkin-Huxley nerve equations. J. Gen. Physiol., 43, p. 867-896. http://dx.doi.org/10.1085/jgp.43.5.867.
Hodgkin, A. L., & Huxley, A. F. (1952). A quantitative description of membrane current and its application to conduction and excitation in nerve. J. Physiol., (117), 500-544. http://dx.doi.org/10.1113/jphysiol.1952.sp004764.
Nagumo, J., Arimoto, S., & Yoshizawa, S. (1962). An active pulse transmission line simulating nerve axon. Proc. IRE., (50), 2061-2070. http://dx.doi.org/10.1109/jrproc.1962.288235.
Phan, V. L. E. (2022). Sufficient Condition for Synchronization in Complete Networks of Reaction-Diffusion Equations of Hindmarsh-Rose Type with Linear Coupling. IAENG International Journal of Applied Mathematics, vol. 52, no. 2, 315-319.
Phan, V. L. E. (2023). Sufficient Condition for Synchronization in Complete Networks of n Reaction-Diffusion Systems of Hindmarsh-Rose Type with Nonlinear Coupling. Engineering Letters, vol. 31, no. 1, 413-418.