Related papers: Pulse Dynamics in Coupled Excitable FIbers: Solito…
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…
We demonstrate that pulses of linear physical systems, weakly perturbed by nonlinear dissipation, exhibit soliton-like behavior in fast collisions. The behavior is demonstrated for linear waveguides with weak cubic loss and for systems…
Excitable pulses are among the most widespread dynamical patterns that occur in many different systems, ranging from biological cells to chemical reactions and ecological populations. Traditionally, the mutual annihilation of two colliding…
According to the conventional approach to model neural ensembles the extracellular environment has fixed ionic concentrations. However, in many cases the extracellular concentration of potassium ions can not be regarded as constant. That…
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…
In this paper, we study an excitable, biophysical system that supports wave propagation of nerve impulses. We consider a slow-fast, FitzHugh-Rinzel neuron model where only the membrane voltage interacts diffusively, giving rise to the…
Pulsating behavior is a universal phenomenon in versatile fields. In nonlinear dissipative systems, the solitons could also pulsate under proper conditions and show many interesting dynamics. However, the pulsation dynamics is generally…
We study the phenomenological model of ensemble of two FitzHugh-Nagumo neuron-like elements with symmetric excitatory couplings. The main advantage of proposed model is the new approach to model of coupling which is implemented by smooth…
A numerical fluid simulation investigation of the temporal evolution of a special class of traveling wave solution of the one dimensional relativistic cold plasma model is reported.The solutions consist of coupled electromagnetic and plasma…
Some mechanisms of cardiac arrhythmias can be presented as a composition of elementary acts of block and reflection on the contacts of homogeneous areas of the conducting tissue. For study this phenomena we use an axiomatic one-dimensional…
We use Molecular Dynamics combined with Dissipative Particle Dynamics to construct a model of a binary mixture where the two species differ only in their dynamic properties (friction coefficients). For an asymmetric mixture of slow and fast…
The present study investigates the spatio-temporal variability in the dynamics of self-sustained supersonic reaction waves propagating through an excitable medium. The model is an extension of Fickett's detonation model with a state…
We study the collective dynamics of an ensemble of coupled identical FitzHugh--Nagumo elements in their excitable regime. We show that collective firing, where all the elements perform their individual firing cycle synchronously, can be…
We study the effects of nonlocal control of pulse propagation in excitable media. As a generic example for an excitable medium the FitzHugh-Nagumo model with diffusion in the activator variable is considered. Nonlocal coupling in form of an…
The dynamical properties and diffusive behavior of a collection of mutually interacting particles are numerically investigated for two types of long-range interparticle interactions: Coulomb-electrostatic and dipole-electrodynamic. It is…
We investigate two types of nonlinear interaction between collinear femtosecond laser pulses with power slightly above the critical for self-focusing $P_{cr}$. In the first case we study energy exchange between filaments. The model…
We study a system of nonlinear differential equations simulating transport phenomena in active media. The model we are interested in is a generalization of the celebrated FitzHugh-Nagumo system, describing the nerve impulse propagation in…
Superconducting state dynamics following excitation of a superconductor with a femtosecond optical pulse is studied in terms of a phenomenological Rothwarf and Taylor model. Analytical solutions for various limiting cases are obtained. The…
We present initial results regarding the existence, stability and interaction of linear and nonlinear vibrational modes in a system of two coupled, one dimensional lattices with unequal numbers of masses. The effects on these nonlinear…
The FitzHugh-Nagumo equation, originally conceived in neuroscience during the 1960s, became a key model providing a simplified view of excitable neuron cell behavior. Its applicability, however, extends beyond neuroscience into fields like…