<p style='text-indent:20px;'>In this work we study the synchronization of ring-structured cellular neural networks modeled by lattice FitzHugh-Nagumo equations with boundary feedback. Through uniform estimates solutions and analysis dissipative dynamics, type is proved under condition that gap signal exceeds adjustable threshold.</p>

We investigated self-organized patterns formed by a FitzHugh–Nagumo model in three-dimensional space. We found functional orders in the model. The edge plane structure was autonomously extracted from an initial cubic pattern. As in a two-dimensional model, the edge points and edge lines developed spontaneously in this model. These edge structures were obtained when parameters were in a specific...

System of signals propagation from one neuron to other represent event of very complex electrochemical mechanism. In this work, we studied the dynamics of modified FitzHugh-Nagumo multi neuron model with sinusoidal external stimulation. In this paper, the coupled model is established on the basis of spiking neuron model, and then the relation of bidirectional coupling strength of the gap juncti...

The simplest models used to describe physical systems are often linear. However, several natural phenomena can only be accurately modeled by relatively complex nonlinear systems of equations. There is a wealth of interesting dynamics displayed by systems consisting of nonlinear elements, for example systems in which the dynamics depend delicately on the initial conditions, viz, chaos, and syste...

In this paper we study a system of stochastic differential equations with dissipative nonlinearity which arise in certain neurobiology models. Besides proving existence, uniqueness and continuous dependence on the initial datum, we shall be mainly concerned with the asymptotic behaviour of the solution. We prove the existence of an invariant ergodic measure ν associated with the transition semi...

A b s t r a c t . We examine the effects of changing the coefficient of variation (CV) of the inter-stimulus interval on the CV of the output interspike interval (ISI), using constant magnitude, supra-threshold pointprocess stimuli of the membrane potential variable in the FitzHughNagumo model. The coefficient of variation of the input is changed within the context of a displaced exponential di...

We consider an idealized network, formed by N neurons individually described by the FitzHugh-Nagumo equations and connected by electrical synapses. The limit for N → ∞ of the resulting discrete model is thoroughly investigated, with the aim of identifying a model for a continuum of neurons having an equivalent behaviour. Two strategies for passing to the limit are analysed: i) a more convention...

Existence and dynamics of chaotic pulses on 1D lattice are discussed. Traveling pulses arise typically in reaction diffusion systems like the FitzHugh-Nagumo equations. Such pulses annihilate when they collide each other. A new type of traveling pulse has been found recently in many systems where pulses bounce off like elastic balls. We consider the behavior of such a localized pattern on 1D la...

The wavefront profile and the propagation velocity of waves in an experimentally observed Belousov-Zhabotinskii reaction are analyzed and a revised FitzHumgh-Nagumo(FHN) model of these systems is identified. The ratio between the excitation period and the recovery period, for a solitary wave are studied, and included within the model. Averaged travelling velocities at different spatial position...

We study several aspects of FitzHugh-Nagumo’s (FH-N) equations without diffusion. Some global stability results as well as the boundedness of solutions are derived by using a suitably defined Lyapunov functional. We show the existence of both supercritical and subcritical Hopf bifurcations. We demonstrate that the number of all bifurcation diagrams is 8 but that the possible sequential occurren...