We analyze the influence of an external sound source in a network FitzHugh-Nagumo oscillators with empirical structural connectivity measured healthy human subjects. report synchronization patterns, induced by frequency source. show that level synchrony can be enhanced choosing and its amplitude as control parameters for patterns. discuss minimum model elucidating modalities music on brain.

In this paper, we present a study of some high-order compact difference schemes for solving the Fitzhugh-Nagumo equations governed by two coupled time-dependent nonlinear reaction diffusion equations in two variables. Solving the Fitzhugh-Nagumo equations is quite challenging, since the equations involve spatial and temporal dynamics in two different scales and the solutions exhibit shock-like ...

Many central neurons, and in particular certain brainstem aminergic neurons exhibit spontaneous and fairly regular spiking with frequencies of order a few Hz. A large number of ion channel types contribute to such spiking so that accurate modeling of spike generation leads to the requirement of solving very large systems of differential equations, ordinary in the first instance. Since analysis ...

In this paper, a solution of the mathematical model an autowave process in thin nearelectrode layer magnetic fluid is found. A modification FitzHugh–Nagumo system taken as basis made it possible to obtain results similar full-scale experiment. As criterion for adequacy model, we use visual correspondence experiment and presence typical phenomena observed process, such reverbs, pacemakers, bypas...

We study Hopf bifurcation solutions to the Monodomain model equipped with FitzHughNagumo cell dynamics. This reaction-diffusion system plays an important role in the field of electrocardiology as a tractable mathematical model of the electrical activity in the human heart. In our setting the bounded spatial domain consists of two subdomains: a collection of automatic cells surrounded by collect...

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...

Statistical complexity measures are used to detect noise-induced order and to quantify stochastic and coherence resonances. We illustrate the method with two paradigmatic models, one of a Brownian particle in a sinusoidally modulated bistable potential, and the other, the FitzHugh-Nagumo model of excitable systems. The method can be employed for the precise detection of subtle signatures of noi...

The paper deals with a semilinear integrodifferential equation that characterizes several dissipative models of Viscoelasticity, Biology and Superconductivity. The initial boundary problem with Neumann conditions is analyzed. When the source term F is a linear function, then the explicit solution is obtained. When F is non linear, some results on existence, uniqueness and a priori estimates are...

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...