Related papers: Parametric Autoresonance with Time-Delayed Control
It is shown, that retardation in the $\alpha$-quenching in the Parker's dynamo model leads to parametric resonance. This result is observed in the numerical simulations and can be reproduced in the simple analytic model. The other…
Systems with time-delayed chaotic dynamics are common in nature, from control theory to aeronautical propulsion. The overarching objective of this paper is to compute the stability properties of a chaotic dynamical system, which is…
System of differential equations describing the initial stage of the capture of oscillatory systems into the parametric autoresonance is considered. Of special interest are solutions whose amplitude increases without bound with time. The…
We study the possibility to stabilize unstable steady states and unstable periodic orbits in chaotic fractional-order dynamical systems by the time-delayed feedback method. By performing a linear stability analysis, we establish the…
Combined effects of the damping and forcing in the underdamped time-delayed Duffing oscillator are considered in this paper. We analyze the generation of a certain damping-induced unpredictability, due to the gradual suppression of…
Results on continuous dependence on parameters, as well as on regularization, of solutions to linear systems of parabolic partial differential equations of second order with delay are given. One of the main features is that the topology on…
Using the model of a generalized Van der Pol oscillator in the regime of subcritical Hopf bifurcation we investigate the influence of time delay on noise-induced oscillations. It is shown that for appropriate choices of time delay either…
We study the stability of general $n$-dimensional nonautonomous linear differential equations with infinite delays. Delay independent criteria, as well as criteria depending on the size of some finite delays are established. In the first…
A mathematical model describing the capture of nonlinear systems into the autoresonance by a combined parametric and external periodic slowly varying perturbation is considered. The autoresonance phenomenon is associated with solutions…
We investigate synchronization between two unidirectionally linearly coupled chaotic non-identical time-delayed systems and show that parameter mismatches are of crucial importance to achieve synchronization. We establish that independent…
We study a conservative system of two nonlinear coupled oscillators. The eigenmodes of the system are thus nonlinearly coupled, and one of them may induce a parametric amplification of the other, called an autoparametric resonance of the…
Effects of time-delayed-feedback on pattern formation are studied in symmetrical bistable media. The results show that the time delay alters the behavior of the front bifurcation remarkably. The critical point of the Nonequilibrium…
It is difficult to analyze the stability of systems with time-varying delays. One approach is to construct a time-transformation that converts the system into a form with a constant delay but with a time-varying scalar appearing in the…
In this work, we study the stabilization of the wave equation using an internal delayed potential. Interestingly, the stabilization mechanism is entirely induced by the delay, since exponential stabilization cannot be achieved in its…
There are several results on the stability of nonlinear positive systems in the presence of time delays. However, most of them assume that the delays are constant. This paper considers time-varying, possibly unbounded, delays and…
We investigated the effect of time delays on phase configurations in a set of two-dimensional coupled phase oscillators. Each oscillator is allowed to interact with its neighbors located within a finite radius, which serves as a control…
Artificial time delay controller was conceptualised for nonlinear systems to reduce dependency on precise system modelling unlike the conventional adaptive and robust control strategies. In this approach unknown dynamics is compensated by…
The stabilization of nonautonomous parabolic equations is achieved by feedback inputs tuning a finite number of actuators, where it is assumed that the input is subject to a time delay. To overcome destabilizing effects of the time delay,…
In this work, we develop an analytical framework to explain the influence of dissipation and detuning parameters on the emergence and stability of autoresonance in a strongly nonlinear weakly damped chain subjected to harmonic forcing with…
We discuss applications of time-delayed feedback control to delay-coupled neural systems and lasers, in the framework of the FitzHugh-Nagumo neuron model and the Lang-Kobayashi laser model, respectively. In the context of neural systems, we…