Related papers: Parametric Autoresonance with Time-Delayed Control
We investigate parametric autoresonance: a persisting phase locking which occurs when the driving frequency of a parametrically excited nonlinear oscillator slowly varies with time. In this regime, the resonant excitation is continuous and…
The present paper examines the active control of parametric resonance in modified Rayleigh-Duffing oscillator. We used the method of averaging to obtain steady-state solutions. We have found the critical value of the parametrical amplitude…
A mathematical model describing the initial stage of the capture into the parametric autoresonance in nonlinear oscillating systems with a dissipation is considered. Solutions with unboundedly growing energy in time at infinity are…
A particularly simple setup is introduced to study the influence of time-delayed coherent feedback on the optical squeezing properties of the degenerate parametric amplifier (DPA). The possibility for significantly enhanced squeezing is…
Autoresonance is a phase locking phenomenon occurring in nonlinear oscillatory system, which is forced by oscillating perturbation. Many physical applications of the autoresonance are known in nonlinear physics. The essence of the…
A mathematical model describing the initial stage of the capture of oscillatory systems into autoresonance under the action of slowly varying pumping is considered. Solutions with an infinitely growing amplitude are associated with the…
The phenomenon of delay-induced resonance implies that in a nonlinear system a time-delay term may be used as an effective enhancer of the oscillations caused by an external forcing maintaining the same frequency. This is possible for the…
Autoresonance is a phase locking phenomenon occurring in nonlinear oscislatory system, which is forced by oscillating perturbation. Many physical applicatcons of the autoresonance are known in nonlenear physics. The essence of the…
We study the periodic forced response of a system of two limit cycle oscillators that interact with each other via a time delayed coupling. Detailed bifurcation diagrams in the parameter space of the forcing amplitude and forcing frequency…
Discrete-time systems under aperiodic sampling may serve as a modeling abstraction for a multitude of problems arising in cyber-physical and networked control systems. Recently, model- and data-based stability conditions for such systems…
We study the stability of unstable steady states in scalar retarded time-delayed systems subjected to a variable-delay feedback control. The important aspect of such a control problem is that time-delayed systems are already…
We study theoretically a bistable systems with time-delayed feedback driven by weak periodic force. The effective potential function and the steady-state probability density are derived. The delay time and the strength of its feedback can…
Time--delayed feedback is exploited for controlling noise--induced motion in coherence resonance oscillators. Namely, under the proper choice of time delay, one can either increase or decrease the regularity of motion. It is shown that in…
The excitation of large amplitude nonlinear waves is achieved via parametric autoresonance of Faraday waves. We experimentally demonstrate that phase locking to low amplitude driving can generate persistent high-amplitude growth of…
Understanding how time delays impact the stability of a delay differential equation is important for modeling many natural and technological systems that experience time delays. Here we introduce a new stability criterion for…
Much recent progress has been achieved for stabilization of linear and nonlinear systems with input delays that are long and dependent on either time or the plant state---provided the dependence is known. In this paper we consider the delay…
In our manuscript, we develop a new approach for stability analysis of one-dimensional wave equation with time delay. The major contribution of our work is to develop a new method for spectral analysis. We derive sufficient and necessary…
We present an analysis of time-delayed feedback control used to stabilize an unstable steady state of a neutral delay differential equation. Stability of the controlled system is addressed by studying the eigenvalue spectrum of a…
We detail in this article the necessity of a change of paradigm for the delay-robust control of systems composed of two linear first order hyperbolic equations. One must go back to the classical trade-off between convergence rate and…
A mathematical model of autoresonance in nonlinear systems with combined parametric and external chirped frequency excitation is considered. Solutions with a growing amplitude and a bounded phase mismatch are associated with the…