This work explores four nonlinear classical models of neural oscillators, the HodgkinHuxley model, the Fitzhugh-Nagumo model, the Morris-Lecar model, and the Hindmarsh-Rose model. Nonlinear contraction theory is used to develop observers and perform synchronization analysis on these systems. Neural oscillation and signaling models are based on the biological function of the neuron, with behavio...

FitzHugh-Nagumo (FHN) model is a famous Reaction-Diffusion System which first introduced for the conduction of electrical impulses along a nerve fiber. This model is also considered as an abstract model for pattern formation. Here, we have used the Cellular Automata method to simulate the pattern formation of the FHN model. It is shown that the pattern of this model is very similar to those...

In this paper, a FitzHugh-Nagumo model with time delays is investigated. The linear stability of the equilibrium and the existence of Hopf bifurcation with delay τ is investigated. By applying Nyquist criterion, the length of delay is estimated for which stability continues to hold. Numerical simulations for justifying the theoretical results are illustrated. Finally, main conclusions are given...

We study the rotating wave patterns in an excitable medium in a disk. This wave pattern is rotating along the given disk boundary with a constant angular speed. To study this pattern we use the wave front interaction model proposed by Zykov in 2007. This model is derived from the FitzHugh-Nagumo equation and it can be described by two systems of ordinary differential equations for wave front an...

In a modified FitzHugh—Nagumo model for excitable tissue a spiral wave is found to break up into an irregular spatial pattern. The main difference between our equations and the standard FitzHugh—Nagumo model is that we use two different time constants: one for the relative refractory period and another for the absolute refractory period. Breakup occurs when the relative refractory period is sho...

This paper studies the solutions of a reaction–diffusion system with nonlinearities that generalise the Lengyel–Epstein and FitzHugh–Nagumo nonlinearities. Sufficient conditions are derived for the global asymptotic stability of the system’s solutions and confirmed through numerical Examples.

The FitzHugh-Nagumo equations have been used as a caricature of the Hodgkin-Huxley equations of neuron firing and to capture, qualitatively, the general properties of an excitable membrane. In this paper, we utilize a modified version of the FitzHugh-Nagumo equations to model the spatial propagation of neuron firing; we assume that this propagation is (at least, partially) caused by the cross-d...

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...