Related papers: Instabilities of localized structures in dissipati…
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…
The Brusselator reaction-diffusion model is a paradigm for the understanding of dissipative structures in systems out of equilibrium. In the first part of this paper, we investigate the formation of stationary localized structures in the…
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 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…
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…
We consider a paradigmatic nonvariational scalar Swift-Hohenberg equation that describes short wavenumber or large wavelength pattern forming systems. This work unveils evidence of the transition from stable stationary to moving localized…
The stability of functional differential equations under delayed feedback is investigated near a Hopf bifurcation. Necessary and sufficient conditions are derived for the stability of the equilibrium solution using averaging theory. The…
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 study the effects of time delayed linear and nonlinear feedbacks on the dynamics of a single Hopf bifurcation oscillator. Our numerical and analytic investigations reveal a host of complex temporal phenomena such as phase slips,…
We study the dynamics of a piecewise-linear second-order delay differential equation that is representative of feedback systems with relays (switches) that actuate after a fixed delay. The system under study exhibits strong…
Neural field equations are integro-differential systems describing the macroscopic activity of spatially extended pieces of cortex. In such cortical assemblies, the propagation of information and the transmission machinery induce…
Motivated by the observation of localized circular excitations (`oscillons') in vertically vibrated granular layers (P.B. Umbanhowar, F. Melo and H.L. Swinney, Nature 382 (1996) 793), we numerically investigate an extension of a…
In this work we propose a feedback approach to regulate the chaotic behavior of the whole family of the generalized Lorenz system, by designing a nonlinear delayed feedback control. We first study the effect of the delay on the dynamics of…
We study the effects of discrete, randomly distributed time delays on the dynamics of a coupled system of self-propelling particles. Bifurcation analysis on a mean field approximation of the system reveals that the system possesses patterns…
Dynamical systems with complex delayed interactions arise commonly when propagation times are significant, yielding complicated oscillatory instabilities. In this Letter, we introduce a class of systems with multiple, hierarchically long…
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…
We study a scalar, first-order delay differential equation (DDE) with instantaneous and state-dependent delayed feedback, which itself may be delayed. The state dependence introduces nonlinearity into an otherwise linear system. We…
The present paper addresses the swing equation with additional delayed damping as an example for pendulum-like systems. In this context, it is proved that recurring sub- and supercritical Hopf bifurcations occur if time delay is increased.…
Reaction delays are important in determining the qualitative dynamical properties of a platoon of vehicles traveling on a straight road. In this paper, we investigate the impact of delayed feedback on the dynamics of the Modified Optimal…
We review some properties of dynamical systems with slowly varying parameters, when a parameter is moved through a bifurcation point of the static system. Bifurcations with a single zero eigenvalue may create hysteresis cycles, whose area…