Related papers: Stability of localized wave fronts in bistable sys…
We study the effect of metastable states on the relaxation process (and hence information propagation) in locally coupled and boundary-driven structures. We first give a general argument to show that metastable states are inevitable even in…
We study the waves at the interface between two thin horizontal layers of immiscible fluids subject to high-frequency horizontal vibrations. Previously, the variational principle for energy functional, which can be adopted for treatment of…
The behavior of two-dimensional coupled map lattices is studied with respect to the global stabilization of unstable local fixed points without external control. It is numerically shown under which circumstances such inherent global…
We consider the resonant system of amplitude equations for the conformally invariant cubic wave equation on the three-sphere. Using the local bifurcation theory, we characterize all stationary states that bifurcate from the first two…
In this paper, we study the numerical stabilization of a 1D system of two wave equations coupled by velocities with an internal, local control acting on only one equation. In the theoretical part of this study, we distinguished two cases.…
The evolution of the amplitude of two nonlinearly interacting waves is considered, via a set of coupled nonlinear Schroedinger-type equations. The dynamical profile is determined by the wave dispersion laws (i.e. the group velocities and…
In this work, we consider a system of two wave equations coupled by velocities in one-dimensional space, with one boundary fractional damping. First, we show that the system is strongly asymptotically stable if and only if the coupling…
We describe various types of traveling fronts of bistable reaction-diffusion cellular automata. These dynamical systems with discrete time, space, and state spaces can be seen as fully discrete versions of widely studied bistable…
The instability and nonlinear evolution of directional ocean waves is investigated numerically by means of simulations of the governing kinetic equation for narrow-band surface waves. Our simulation results reveal the onset of the…
We develop a new method to isolate localized defects from extended vibrational modes in disordered solids. This method augments particle interactions with an artificial potential that acts as a high-pass filter: it preserves small-scale…
Planar travelling waves on $\mathbb R^d,$ with $ d\geq 2,$ are shown to persist in systems of reaction-diffusion equations with multiplicative noise on significantly long timescales with high probability, provided that the wave is orbitally…
We study the stabilization of localized structures by discreteness in one-dimensional lattices of diffusively coupled nonlinear sites. We find that in an external driving field these structures may lose their stability by either relaxing to…
Localization of waves by disorder is a fundamental physical problem encompassing a diverse spectrum of theoretical, experimental and numerical studies in the context of metal-insulator transition, quantum Hall effect, light propagation in…
Biological active matter is typically tightly coupled to chemical reaction networks affecting its assembly-disassembly dynamics and stress generation. We show that localized states can emerge spontaneously if assembly of active matter is…
We consider reaction-diffusion systems with multiplicative noise on a spatial domain of dimension two or higher. The noise process is white in time, coloured in space, and invariant under translations. In the deterministic setting,…
The dynamical behavior of switched affine systems is known to be more intricate than that of the well-studied switched linear systems, essentially due to the existence of distinct equilibrium points for each subsystem. First, under…
The emergence of hydrodynamic bend instabilities in ordered suspensions of active particles is widely observed across diverse living and synthetic systems, and is considered to be governed by dipolar active stresses generated by the…
Microwave spectroscopy of individual vortex-state magnetic nano-disks in a perpendicular bias magnetic field, $H$, is performed using a magnetic resonance force microscope (MRFM). It reveals the splitting induced by $H$ on the gyrotropic…
In this paper, we focus on the existence of propagation fronts, solutions to non-local dispersion reaction models. Our aim is to provide a unified proof of this existence in a very broad framework using simple real analysis tools. In…
Linear stability of stratified two-phase flows in horizontal channels to arbitrary wavenumber disturbances is studied. The problem is reduced to Orr-Sommerfeld equations for the stream function disturbances, defined in each sublayer and…