In this paper, we established traveling wave solutions of the nonlinear evolution equation. The sine-cosine method was used to construct travelling wave solutions of the Fitzhugh-Nagumo equation and Cahn-Allen equation. Graphical interpretation shows that obtained results include periodic and Soliton wave solutions. It is also shown that for α =−1, solutions of Fitzhugh-Nagumo equation coincide...

We present a novel mathematical approach to model noise in dynamical systems. We do so by considering dynamics of a chain of diffusively coupled Nagumo cells affected by noise. We show that the noise in transmembrane current can be effectively modelled as fluctuations in electric characteristics of the membrane. The proposed approach to model noise in a nerve fibre is different from the standar...

With a modulated CO2 laser as a standard model of periodically driven multistable systems, we experimentally demonstrate that a small-amplitude optoelectronic feedback perturbation can efficiently transform a bursting chaotic system to a nonchaotic one. Numerical simulations are in excellent agreement with the experimental results. The control has also been equally effective in the case of a dr...

We investigate the effects of cross-diffusion on propagating waves in an activator-inhibitor system. The model consists of a piecewise linear approximation of FitzHugh-Nagumo kinetics and a cross-diffusion term for either the activator or the inhibitor. We obtain exact analytic solutions for traveling fronts and solitary pulses and discuss the corresponding speed diagrams. A detailed comparison...

Trigger waves are a recurring biological phenomenon involved in transmitting information quickly and reliably over large distances. Well-characterized examples include action potentials propagating along the axon of a neuron, calcium waves in various tissues, and mitotic waves in Xenopus eggs. Here we use the FitzHugh-Nagumo model, a simple model inspired by the action potential that is widely ...

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...

Abstract In Chapter 6, we studied a simple version of the cable equation, where diffusion term was added to FitzHugh-Nagumo equations. this chapter, will revisit equation and go through derivation model. addition, consider numerical solution for neuronal axon with membrane dynamics modeled by Hodgkin-Huxley

6 Winnerless competition is a theoretical model used to study cognitive and 7 attention-based processes using the sequential switching between 8 metastable states of a neurodynamical system. This competition is observed 9 in both physical neural networks and in higher-ordered cognition. I 10 demonstrate this principle in a network of three interconnected Fitzhugh11 Nagumo neurons and in the wor...

Small lattices of N nearest-neighbor coupled excitable FitzHugh-Nagumo systems, with time-delayed coupling are studied and compared with systems of FitzHugh-Nagumo oscillators with the same delayed coupling. Bifurcations of equilibria in an N=2 case are studied analytically, and it is then numerically confirmed that the same bifurcations are relevant for the dynamics in the case N>2. Bifurcatio...