相关论文: Stationary localized structures and the effect of …
We report on a novel behavior of solitary localized structures in a real Swift-Hohenberg equation subjected to a delayed feedback. We shall show that variation in the product of the delay time and the feedback strength leads to nontrivial…
We investigate the dynamics of a single breathing localized structure in a three-component reaction-diffusion system subjected to the time-delayed feedback. We show that variation of the delay time and the feedback strength can lead either…
We investigate a control of the motion of localized structures of light by means of delay feedback in the transverse section of a broad area nonlinear optical system. The delayed feedback is found to induce a spontaneous motion of a…
The Brusselator is a generic reaction-diffusion model for a tri-molecular chemical reaction. We consider the case when the input and output reactions are slow. In this limit, we show the existence of $K$-periodic, spatially bi-stable…
We present a linear model, which mimics the response of a spatially extended dissipative medium to a distant perturbation, and investigate its dynamics under delayed feedback control. The time a perturbation needs to propagate to a…
An activator-inhibitor-substrate model of side-branching used in the context of pulmonary vascular and lung development is considered on the supposition that spatially localized concentrations of the activator trigger local side-branching.…
We prove that the famous diffusive Brusselator model can support more complicated spatial-temporal wave structure than the usual temporal-oscillation from a standard Hopf bifurcation. In our investigation, we discover that the diffusion…
We consider a stochastic version of the so-called Brusselator - a mathematical model for a two-dimensional chemical reaction network - in which one of its parameters is assumed to vary randomly. It has been suggested via numerical…
A theoretical framework is developed for a precise control of spatial patterns in oscillatory media using nonlinear global feedback, where a proper form of the feedback function corresponding to a specific pattern is predicted through the…
We consider a bulk-membrane-coupled partial differential equation in which a single diffusion equation posed within the unit ball is coupled to a two-component reaction diffusion equation posed on the bounding unit sphere through a linear…
{We investigate the space-time dynamics of a Vertical-Cavity Surface-Emitting Laser (VCSEL) subject to optical injection and to delay feedback control. Apart from their technological advantages, broad area VCSELs allow creating localized…
This article describes a reduction of a nonautonomous Brusselator reaction-diffusion system of partial differential equations on a spherical cap with time dependent curvature using the method of centre manifold reduction. Parameter values…
In the singularly perturbed limit corresponding to a large diffusivity ratio between two components in a reaction-diffusion (RD) system, quasi-equilibrium spot patterns are often admitted, producing a solution that concentrates at a…
A stochastic version of the Brusselator model is proposed and studied via the system size expansion. The mean-field equations are derived and shown to yield to organized Turing patterns within a specific parameters region. When determining…
Localized states are a universal phenomenon observed in spatially distributed dissipative nonlinear systems. Known as dissipative solitons, auto-solitons, spot or pulse solutions, these states play an important role in data transmission…
We show analytically and numerically that time delayed nonlocal response induces traveling localized states in bistable systems. These states result from fronts interaction. We illustrate this mechanism in a generic bistable model with a…
We study how nonlinear delayed-feedback in the Ikeda model can induce solitary impulses, i.e. dissipative solitons. The states are clearly identified in a virtual space-time representation of the equations with delay, and we find that…
We consider a wide-aperture surface-emitting laser with a saturable absorber section subjected to time-delayed feedback. We adopt the mean-field approach assuming a single longitudinal mode operation of the solitary VCSEL. We investigate…
In this work we study the Brusselator - a prototypical model for chemical oscillations - under the assumption that the bifurcation parameter is of order $O(1/\epsilon)$ for positive $\epsilon\ll 1$. The dynamics of this mathematical model…
We report on the dynamics of localized structures in an inhomogeneous Swift-Hohenberg model describing pattern formation in the transverse plane of an optical cavity. This real order parameter equation is valid close to the second order…