We consider a FitzHugh-Nagumo Reaction-Diffusion type system (FHN). The dynamics of the reaction part induces a unique repulsive stationnary point (0, 0) and a unique attractive limit cycle. After a description of the asymptotic behaviour of the FHN system, we deal with the synchronization and control analysis of N coupled FHN systems.

In this paper, we make some analysis on the FitzHugh-Nagumo model and improve it to build a neural network, and the network is used to implement visual selection and attention shifting. Each group of neurons representing one object of a visual input is synchronized; different groups of neurons representing different objects of a visual input are desynchronized. Cooperation and competition mecha...

Chaos is an important applied area in nonlinear dynamical systems and it is applicable to many real-world systems including the biological systems. Nerve membranes are known to exhibit their own nonlinear dynamics which generate and propagate action potentials. Such nonlinear dynamics in nerve membranes can produce chaos in neurons and related bifurcations. In 1952, A.L. Hodgkin and A.F. Huxley...

We provide an asymptotically justified derivation of activity measure evolution equations (AMEE) for a finite size neural network. The approach takes into account the dynamics for each isolated neuron in the network being modeled by a biophysical model, i.e. Hodgkin-Huxley equations or their reductions. By representing the interacting network as self and pairwise interactions, we propose a gene...

This paper investigates travelling wave solutions of the FitzHugh-Nagumo equation from the viewpoint of fast-slow dynamical systems. These solutions are homoclinic orbits of a three dimensional vector field depending upon system parameters of the FitzHugh-Nagumo model and the wave speed. Champneys et al. [A.R. Champneys, V. Kirk, E. Knobloch, B.E. Oldeman, and J. Sneyd, When Shilnikov meets Hop...

The work concerns the multiscale modeling of a nerve fascicle myelinated axons. We present rigorous derivation macroscopic bidomain model describing behavior electric potential in based on FitzHugh–Nagumo membrane dynamics. approach is two-scale convergence machinery combined with method monotone operators.