We show how a variety of stable spatio-temporal periodic patterns can be created in 2D-lattices of coupled oscillators with non-homogeneous coupling delays. The results are illustrated using the FitzHugh-Nagumo coupled neurons as well as coupled limit cycle (Stuart-Landau) oscillators. A "hybrid dispersion relation" is introduced, which describes the stability of the patterns in spatially exten...

Neuron physiology is actually described using the well known models created by Hodgkin-Huxley (HH) and their derivatives which came later, the Fitzhugh-Nagumo (FN) equations. These attempts to understand the internal functioning of the neuron are unfortunately far from the strict Nature's observation. These equations, particularly, are unable to explain an unidirectional propagation of action p...

We focus on the qualitative analysis of a reaction-diffusion with spatial heterogeneity near a bifurcation. The system is a generalization of the well known FitzHugh-Nagumo system in which the excitability parameter is space dependent. This heterogeneity allows to exhibit concomitant stationary and oscillatory phenomena. We prove the existence of an Hopf bifurcation and determine an equation of...

A FitzHugh–Nagumo type spiking neuron model equipped with an asymmetric activation function is investigated. An analogue nonlinear electrical circuit imitating the dynamics of the model is proposed. It is demonstrated that a simple first order linear filter coupled to the system can inhibit spiking and stabilize the system on an unstable steady state, the position of which is not required to be...

Thermo-optical pulsing in semiconductor amplifiers is experimentally shown to correspond to a very common excitable scenario (the van der Pol-Fitzhugh-Nagumo system). Self-sustained oscillations appear in the sequence predicted by this simple dynamical model as we change either the injection level or the bias current. Periodic modulation of these parameters leads to the characteristic phase-loc...

The pioneering work of Hodgkin and Huxley (1952), and subsequent investigations, has established that good mathematical models for the conduction of nerve impulses along an axon can be given. These models take the form of a system of ordinary differential equations, coupled to a diffusion equation. Simpler models, which seem to describe the qualitative behavior, have been proposed by FitzHugh a...

Due to the encouraging increase in their applications, control theory [Lefschetz, 1965] and [Narendra et al., 1973], design of electric circuits [Chua et al., 1990], neurobiology [FitzHugh, 1961] and [Nagumo et al., 1962] piecewise linear differential systems were studied early from the point of view of qualitative theory of ordinary differential equations [Andronov et al., 1966]. Nowadays, a l...