Related papers: On propagation failure in 1 and 2 dimensional exci…
In this paper, we report on the generation and propagation of traveling pulses in a homogeneous network of diffusively coupled, excitable, slow-fast dynamical neurons. The spatially extended system is modelled using the nearest neighbor…
We report an asymmetric behavior of optical pulses during their propagation through a time-varying linear optical medium. The refractive index of the medium is considered to be varying with time and complex such that a sufficient amount of…
We study the dynamics of a reaction-diffusion system composed of two mutually coupled excitable fibers. We focus on the situation in which dynamical properties of the two fibers are not identical because of the parameter difference between…
Propagation of pulses in myelinated fibers may be described by appropriate solutions of spatially discrete FitzHugh-Nagumo systems. In these systems, propagation failure may occur if either the coupling between nodes is not strong enough or…
Magnetic stimulation is a standard tool in brain research and many fields of neurology, as well as psychiatry. From a physical perspective, one key aspect of this method is the inefficiency of available setups. Whereas the spatial field…
We prove the existence of fast traveling pulse solutions in excitable media with non-local coupling. Existence results had been known, until now, in the case of local, diffusive coupling and in the case of a discrete medium, with…
We present an extension of the canonical coupled mode theory of electromagnetic waves to the case of pulses and spatio-temporal perturbations in complex media. Unlike previous attempts to derive such a model, our approach involves no…
We investigate wave propagation in rotationally symmetric tubes with a periodic spatial modulation of cross section. Using an asymptotic perturbation analysis, the governing quasi two-dimensional reaction-diffusion equation can be reduced…
Starting from the wave equation for a medium with material properties that vary periodically, we study a system of recurrence relations that describe propagation of wave packets that oscillate on the microscale (i.e. on lengths of the order…
In cardiac electrophysiology, it is important to predict the necessary conditions for conduction failure, the failure of the cardiac excitation propagation even in the presence of normal excitable tissue, in high-dimensional anisotropic…
Propagation of the extremely short electromagnetic pulse in non-linear dielectric media without the slowly varying envelope approximation is discussed. The models under consideration take into account both resonant and not-resonant…
We develop an effective theory of pulse propagation in a nonlinear {\it and} disordered medium. The theory is formulated in terms of a nonlinear diffusion equation. Despite its apparent simplicity this equation describes novel phenomena…
We present a method to control the two-dimensional shape of traveling wave solutions to reaction-diffusion systems, as e.g. interfaces and excitation pulses. Control signals that realize a pre-given wave shape are determined analytically…
We consider the strength-duration relationship in one-dimensional spatially extended excitable media. In a previous study [Idris and Biktashev 2008] set out to separate initial (or boundary) conditions leading to propagation wave solutions…
In this paper we study the dispersive properties related to a model of peridynamic evolution, governed by a non local initial value problem, in the cases of two and three spatial dimensions. The features of the wave propagation…
We analyze the effects of spatially extended periodic forcing on the dynamics of one-dimensional excitation waves. Entrainment of unstable primary waves has been studied numerically for different amplitudes and frequencies of additional…
We study an intense-short pulse propagation in a saturable cubic-quintic nonlinear media in the presence of nonlinear dispersion within the framework of an extended variational approach. We derive an effective equation for the pulse width…
A method is shown for preventing temporal broadening of ultrafast optical pulses in highly dispersive and fluctuating media for arbitrary signal-pulse profiles. Pulse pairs, consisting of a strong-field control-pulse and a weak-field…
We investigate different mechanical effects which accompany the nerve pulse propagation by using mathematical modeling. The propagation process is composed by three connected phenomena: (i) the action potential (electrical signal) which is…
Models that invoke nonlinear wavefront propagation in a chemically excitable medium are rife in the biological literature. Indeed, the idea that wavefront propagation can serve as a signaling mechanism has often been invoked to explain…