Related papers: Extreme forcing and wave dynamics in weakly nonloc…
It has been reported that traveling waves propagate periodically and stably in sub-excitable systems driven by noise [Phys. Rev. Lett. \textbf{88}, 138301 (2002)]. As a further investigation, here we observe different types of traveling…
The dynamics of spatiotemporal patterns in oscillatory reaction-diffusion systems subject to periodic forcing with a spatially random forcing amplitude field are investigated. Quenched disorder is studied using the resonantly forced complex…
We investigate a ring of $N$ FitzHugh--Nagumo elements coupled in \emph{phase-repulsive} fashion and submitted to a (subthreshold) common oscillatory signal and independent Gaussian white noises. This system can be regarded as a reduced…
Using methods of numerical simulation, we analyze the influence of L\'evy noise on synchronization of excitable oscillators in the regime of coherence resonance. Three cases are under consideration: forced synchronization of a single…
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…
This article communicates results on regular depolarization cascades in periodically-kicked feedforward chains of excitable two-dimensional FitzHugh-Nagumo systems driven by sufficiently strong excitatory forcing at the front node. The…
The FitzHugh-Nagumo (FHN) model serves as a fundamental neuronal model which is extensively studied across various dynamical scenarios, we explore the dynamics of a scalar FHN oscillator under the influence of white noise. Unlike previous…
Using methods of numerical simulation, we demonstrate the constructive role of memristive coupling in the context of the travelling wave formation and robustness in an ensemble of excitable oscillators described by the FitzHugh-Nagumo…
We propose a method to analytically show the possibility for the appearance of a maximum in the signal-to-noise ratio in nonpotential systems. We apply our results to the FitzHugh-Nagumo model under a periodic external forcing, showing that…
We consider synchronization by noise for stochastic partial differential equations which support traveling pulse solutions, such as the FitzHugh-Nagumo equation. We show that any two pulse-like solutions which start from different positions…
This study investigates the dynamics of a globally coupled network of heterogeneous FitzHugh Nagumo (FHN) oscillators under stochastic influences, with particular emphasis on the emergence of extreme events (EE). While previous studies…
In systems that exhibit a bistability between nonlinear traveling waves and the basic state, pairs of fronts connecting these two states can form localized wave pulses whose stability depends on the interaction between the fronts. We…
The Fitzhugh-Nagumo neuronal model is used to explore the influence of the electric field on thermosensitive neurons' dynamics. This study investigates how the electric field affects polarization modulation in cell media induced by changes…
We investigate feedback control of the cooperative dynamics of two coupled neural oscillators that is induced merely by external noise. The interacting neurons are modelled as FitzHugh-Nagumo systems with parameter values at which no…
We study deterministic systems, composed of excitable units of FitzHugh-Nagumo type, that are capable of self-generating and self-terminating strong deviations from their regular dynamics without the influence of noise or parameter change.…
We examine traveling-wave solutions on a regular ring network with one additional long-range link that spans a distance d. The nodes obey the FitzHugh-Nagumo kinetics in the excitable regime. The additional shortcut induces a plethora of…
The use of high-frequency currents in neurostimulation has received increased attention in recent years due to its varied effects on tissues and cells. Nonlinear differential equations are commonly used as models for Neurons, and averaging…
In this paper, we investigate so-called forced wave solutions of a three components reaction-diffusion system from population dynamics. Our system involves three species that are respectively two competing preys and one predator; moreover,…
It is shown that arbitrarily weak (frozen) heterogeneity can induce global synchronized oscillations in excitable media close to threshold. The work is carried out on networks of coupled van der Pol-FitzHugh-Nagumo oscillators. The result…
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…