This paper is devoted to the numerical approximation of spatially extended FitzHugh–Nagumo transport equation with strong local interactions based on a particle method. In this regime, time step can be subject stability constraints related interaction kernel. To avoid limitation, our approach higher-order implicit-explicit schemes. Thus, when magnitude becomes large, method provides consistent ...

This paper treats the question of robust control of chaos in modified FitzHugh–Nagumo neuron model under external electrical stimulation based on internal model principle. We first present the solution of the global robust output regulation problem for output feedback system with nonlinear exosystem. Then we show that the robust control problem for the modified FitzHugh–Nagumo neuron model can ...

Relative equilibria are special solutions of partial differential equations (PDEs), which are stationary in an appropriate comoving frame of reference. Such solutions occur frequently in biological and chemical models, e.g. when describing pattern formation of reaction-diffusion equations. Examples are traveling waves in 1d, planar and spiral waves in 2d and scroll waves in 3d. If the equation ...

We propose a factorization scheme for ordinary differential equations with polynomial nonlinearities (reaction-diffusion in the traveling frame and dampedanharmonic-oscillator equations) which is different and more efficient than that given by L.M. Berkovich in Sov. Math. Dokl. 45, 162 (1992). We then invert the factorization brackets in the SUSYQM style to get ODE’s with a different polynomial...

We study the existence and stability of small-amplitude periodic waves emerging from fold-Hopf equilibria in a system one reaction–diffusion equation coupled with ordinary differential equation. This includes FitzHugh–Nagumo system, caricature calcium models, other models real-world applications. Based on recent results averaging theory, we solve solutions related three-dimensional systems then...

Formal asymptotic expansions have long been used to study the singularly perturbed Allen-Cahn type equations and reaction-diffusion systems, including in particular the FitzHugh-Nagumo system. Despite their successful role, it has been largely unclear whether or not such expansions really represent the actual profile of solutions with rather general initial data. By combining our earlier result...

A Neumann problem in the strip for the Fitzhugh Nagumo system is considered. The transformation in a non linear integral equation permits to deduce a priori estimates for the solution. A complete asymptotic analysis shows that for large t the effects of the initial data vanish while the effects of boundary disturbances φ1(t), φ2(t) depend on the properties of the data. When φ1, φ2 are convergen...