Identical synchronization controller between the Hindmarsh -Rose 2D and the FitzHugh-Nagumo type model

Van Long Em Phan1, , Tan Dat Nguyen1, Minh Phuc Nguyen1, Thi Ngoc Lan Nguyen1
1 An Giang University, Vietnam National University Ho Chi Minh City, Vietnam

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Abstract

Identical synchronization is not easy to get between two different systems of ordinary differential equations even the big coupling strength. In this study, a controller is proposed to help the identical synchronization occur between the model of Hindmarsh-Rose 2D type and the model of FitzHugh-Nagumo type. Specifically, we search for sufficient conditions to achieve the desired synchronization with the introduced controller and simulate it numerically on R to verify its effectiveness.

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References

Aeyels, D. (1995). Asymptotic Stability of Nonautonomous Systems by Lyapunov’s Direct Method. Systems and Control Letters, 25, 273-280. https://doi.org/10.1016/0167-6911(94)00088-D
Aziz-Alaoui, M. A. (2006). Synchronization of Chaos. Encyclopedia of Mathematical Physics, Elsevier, (Vol. 5), 213-226.
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.
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.
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.
Braun, H.A., Wissing, H., Schäfer, K., & Hirsch, M.C. (1994). Oscillation and noise determine signal transduction in shark multimodel sensory cells. Nature, (Vol. 367), p. 270- 273.
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., (Vol. 43), p. 867–896.
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.
Nagumo, J., Arimoto, S., & Yoshizawa, S. (1962). An active pulse transmission line simulating nerve axon. Proc. IRE., (50), 2061–2070.
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.