<p style='text-indent:20px;'>We investigate the formation of stationary patterns in FitzHugh-Nagumo reaction-diffusion system with linear cross-diffusion terms. We focus our analysis on effects Turing mechanism. Linear stability indicates that positive values inhibitor enlarge region parameter space where a instability is excited. A sufficiently large coefficient removes requirement impos...

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

Using the standard van der Pol–FitzHugh–Nagumo excitable medium model, I demonstrate a generic mechanism, diversity, that provokes the emergence of global oscillations from individually quiescent elements in heterogeneous excitable media. This mechanism may be operating in the mammalian pancreas, where excitable b cells, quiescent when isolated, are found to oscillate when coupled, despite the ...

Using the standard van der Pol-FitzHugh-Nagumo excitable medium model, I demonstrate a generic mechanism, diversity, that provokes the emergence of global oscillations from individually quiescent elements in heterogeneous excitable media. This mechanism may be operating in the mammalian pancreas, where excitable beta cells, quiescent when isolated, are found to oscillate when coupled, despite t...

We show that extensive thermostatistics based on Rényi entropy and Kolmogorov–Nagumo averages can be expressed in terms of Tsallis nonextensive thermostatistics. We use this correspondence to generalize thermostatistics to a large class of Kolmogorov–Nagumo means and suitably adapted definitions of entropy. As an application, we reanalyze linguistic data discussed in a paper by Montemurro.  20...

in this work, the solution of a boundary value problem is discussed via asemi analytical method. the purpose of the present paper is to inspect theapplication of the adomian decomposition method for solving the nagumo tele-graph equation. the numerical solution is obtained for some special cases sothat demonstrate the validity of method.

We investigate existence and uniqueness of solutions of a McKeanVlasov evolution PDE representing the macroscopic behaviour of interacting Fitzhugh-Nagumo neurons. This equation is hypoelliptic, nonlocal and has unbounded coefficients. We prove existence of a solution to the evolution equation and non trivial stationary solutions. Moreover, we demonstrate uniqueness of the stationary solution i...

As additivity is a characteristic property of the classical information measure, Shannon entropy, pseudo-additivity of the form x+qy = x+y+(1−q)xy is a characteristic property of Tsallis entropy. Rényi in [1] generalized Shannon entropy by means of Kolmogorov-Nagumo averages, by imposing additivity as a constraint. In this paper we show that there exists no generalization for Tsallis entropy, b...