Synchronization in complete networks of reaction-diffusion equations of Fitzhugh-Nagumo wiht spiral solutions

Van Long Em Phan

Main Article Content

Abstract

Synchronization is a ubiquitous feature in many natural systems and nonlinear science. In this paper, synchronization is studied in complete networks. Each element of the network is represented by a system of FitzHugh-Nagumo reaction-diffusion; especially every subsystem has a spiral-type solution. The result shows that those networks of greater elements synchronize more easily, and their spiral solutions are maintained, but different in forms.

Article Details

References

Ambrosio, B., & Aziz-Alaoui, M. A. (2012), “Synchronization and control of coupled reaction-diffusion systems of the FitzHugh-Nagumo-type”, Computers and Mathematics with Applications, (64), 934-943.
Ambrosio, B., & Aziz-Alaoui, M. A. (March 2013), “Synchronization and control of a network of coupled reaction-diffusion systems of generalized FitzHugh-Nagumo type”, ESAIM: Proceedings, Vol. 39, 15-24.
Aziz-Alaoui, M. A. (2006), “Synchronization of Chaos”, Encyclopedia of Mathematical Physics, Elsevier, 5, 213-226.
Corson, N. (2009), Dynamique d'un modèle neuronal, synchronisation et complexité, Luận án Tiến sĩ, Trường Đại học Le Havre, Pháp.
Ermentrout, G. B., & Terman, D. H. (2009), Mathematical Foundations of Neurosciences, Springer.
Hodgkin, A. L., & Huxley, A. F. (1952), “A quantitative description of membrane current and ts application to conduction and excitation in nerve”, J. Physiol., (117), 500-544.
Izhikevich, E. M. (2007), Dynamical Systems in Neuroscience, The MIT Press.
Keener, J. P., & Sneyd, J. (2009), Mathematical Physiology, Springer.
Murray, J. D. (2010), Mathematical Biology, Springer.
Nagumo, J., Arimoto, S., & Yoshizawa, S. (1962), “An active pulse transmission line simulating nerve axon”, Proc. IRE., (50), 2061-2070.