<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 prove the validity of an averaging principle for a class of systems of slow-fast reaction-diffusion equations with the reaction terms in both equations having polynomial growth, perturbed by a noise of multiplicative type. The models we have in mind are the stochastic Fitzhugh– Nagumo equation arising in neurophysiology and the Ginzburg–Landau equation arising in statistical mechanics.

We study numerically the Turing pattern in three dimensions in a FitzHugh-Nagumo-type reaction-diffusion system. We have found that interconnected periodic domain structures such as a gyroid, Fddd, and perforated lamellar structures appear in three dimensions, which never exist in lower dimensions. The stability analysis of these structures is also performed by means of a mode expansion.

We provide a convergence result for numerical schemes approximating nonlocal front propagation equations. Our schemes are based on a recently investigated notion of weak solution for these equations. We also give examples of such schemes, for a dislocation dynamics equation, and for a Fitzhugh-Nagumo type system.

The reaction-diffusion system of Fitzhugh Nagumo is considered. The initialboundary problems with Neumann and Dirichlet conditions are analyzed. By means of an equivalent semilinear integrodifferential equation which characterizes several dissipative models of viscoelasticity, biology, and superconductivity, some results on existence, uniqueness and a priori estimates are deduced both in the li...

The paper proposes a new mathematical FitzHugh—Nagumo model with memory, which describes the propagation of nerve impulse in membrane. consists an integro-differential equation initial conditions (the Cauchy problem). difference kernel (memory function) was chosen as power function so that it can be rewritten terms fractional derivative. For problem, explicit finite-difference scheme is constru...

Abstract In this paper, we shall study the formation of stationary patterns for a reaction-diffusion system in which FitzHugh-Nagumo (FHN) kinetics, its excitable regime, is coupled to linear cross-diffusion terms. (Gambino et al. Excitable Fitzhugh-Nagumo model with cross-diffusion: long-range activation instabilities, 2023), proved that supports emergence cross-Turing patterns, i.e., close-to...

The aim of this work is to describe the dynamics a fractional-order coupled FitzHugh–Nagumo neuronal model. equilibrium states are analyzed in terms their stability properties, both dependently and independently fractional orders Caputo derivatives, based on recently established theoretical results. Numerical simulations shown clarify exemplify

A controller-propagator system with a FitzHugh–Nagumo equation can be reduced to a free boundary problem when a layer parameter ” is equal to zero. We shall show the existence of solutions and the occurence of a Hopf bifurcation for this free boundary problem as the controlling parameter varies. c © 1999 Elsevier Science B.V. All rights reserved. AMS classi cation: primary 35R35; 35B32; seconda...

We characterize numerically the regime of anticipated synchronization in the coupled FitzHugh-Nagumo model for neurons. We consider two neurons, coupled unidirectionally (in a master-slave configuration), subject to the same random external forcing and with a recurrent inhibitory delayed connection in the slave neuron. We show that the scheme leads to anticipated synchronization, a regime in wh...