Related papers: Triggering synchronized oscillations through arbit…
In assemblies of globally coupled dynamical units, weak noise perturbing independently the individual units can cause anomalous dispersion in the synchronized cloud of the units in the phase space. When the noise-free dynamics of the…
We study the interplay between diversity and noise in a 3D network of FitzHugh-Nagumo elements, with topology and dimensions chosen to model a pancreatic beta-cell cluster, as an example of an excitable cell network. Our results show that…
The influence of time delay in systems of two coupled excitable neurons is studied in the framework of the FitzHugh-Nagumo model. Time-delay can occur in the coupling between neurons or in a self-feedback loop. The stochastic…
We investigate the role of the degree of symmetry of the diversity distribution in shaping the collective dynamics of networks of coupled excitable units modeled by FitzHugh-Nagumo equations. While previous studies have focused primarily on…
The mechanism of phase synchronization between uncoupled limit-cycle oscillators induced by common external impulsive forcing is analyzed. By reducing the dynamics of the oscillator to a random phase map, it is shown that phase…
The dynamics of an oscillator driven by both low- and high- frequency external signals is studied. It is shown that both two- and three-frequency resonances arise due to a nonlinear interaction of these harmonic forces. Conditions which…
We present conclusive evidence showing that different sources of diversity, such as those represented by quenched disorder or noise, can induce a resonant collective behavior in an ensemble of coupled bistable or excitable systems. Our…
This study focuses on extending the concept of weak signal enhancement from dynamical systems based on vibrational resonance of nonlinear systems, to non-smooth systems. A Van der Pol- Duffing oscillator with a one-sided barrier, subjected…
We theoretically describe how weak signals may be efficiently transmitted throughout more than one frequency range in noisy excitable media by kind of stochastic multiresonance. This serves us here to reinterpret recent experiments in…
Noise can induce coherent oscillations in excitable systems without periodic orbits. Here, we establish a method to derive a hybrid system approximating the noise-induced coherent oscillations in excitable systems and further perform phase…
We analyze the effect of small-amplitude noise and heterogeneity in a network of coupled excitable oscillators with strong time scale separation. Using mean-field analysis, we uncover the mechanism of a new nontrivial effect --…
We focus on the long time behavior of complex networks of reaction-diffusion (RD) systems. We prove the existence of the global attractor and a $L^{\infty}$-bound for a network of $n$ RD systems with $d$ variables each. This allows us to…
We investigate the effects of heterogeneous delays in the coupling of two excitable neural systems. Depending upon the coupling strengths and the time delays in the mutual and self-coupling, the compound system exhibits different types 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…
Sub-threshold stimuli cannot initiate excitations in active media, but surprisingly as we show in this paper, they can alter the time-evolution of spatially heterogeneous activity by modifying the recovery dynamics. This results in…
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…
We analyze the influence of an external sound source in a network of FitzHugh-Nagumo oscillators with empirical structural connectivity measured in healthy human subjects. We report synchronization patterns, induced by the frequency of the…
Nonlinear oscillations and synchronisation phenomena are ubiquitous in nature. We study the synchronization of self oscillating magneto-optically trapped cold atoms to a weak external driving. The oscillations arise from a dynamical…
Excitable media are ubiquitous in nature, and in such systems the local excitation tends to self-organize in traveling waves, or in rotating spiral-shaped patterns in two or three spatial dimensions. Examples include waves during a pandemic…
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…