Related papers: Limit Cycles and Chaos Induced by a Nonlinearity w…
We formulate a phase-reduction method for a general class of noisy limit cycle oscillators and find that the phase equation is parametrized by the ratio between time scales of the noise correlation and amplitude relaxation of the limit…
The oscillatory response of nonlinear systems exhibits characteristic phenomena such as multistability, discontinuous jumps and hysteresis. These can be utilized in applications leading, e.g., to precise frequency measurement, mixing,…
We propose a method that is able to analyze chaotic time series, gained from exp erimental data. The method allows to identify scalar time-delay systems. If the dynamics of the system under investigation is governed by a scalar time-delay…
Chemical oscillation is an interesting nonlinear dynamical phenomenon which arises due to complex stability condition of the steady state of a reaction far away from equilibrium which is usually characterised by a periodic attractor or a…
We analyze the stabilization of unstable steady states by delayed feedback control with a periodic time-varying delay in the regime of a high-frequency modulation of the delay. The average effect of the delayed feedback term in the control…
A unified theory of the temporal current self-oscillations is presented. We establish these oscillations as the manifestations of limit cycles, around unstable steady-state solutions caused by the negative differential conductance. This…
We introduce an extension to the standard reduction of oscillatory systems to a single phase variable. The standard reduction is often insufficient, particularly when the oscillations have variable amplitude and the magnitude of each…
Context. Recent observations of decayless transverse oscillations have shown two branches in the relationship between periods and loop lengths. One is a linear relationship, interpreted as a standing mode. The other shows almost no…
This paper studies the effects of distributed delay coupling on the dynamics in a system of non-identical coupled Stuart-Landau oscillators. For uniform and gamma delay distribution kernels, conditions for amplitude death are obtained in…
In order to discover generic effects of heterogeneous communication delays on the dynamics of large systems of coupled oscillators, this paper studies a modification of the Kuramoto model incorporating a distribution of interaction delays.…
We study the effects of noise on the dynamics of a system of coupled self-propelling particles in the case where the coupling is time-delayed, and the delays are discrete and randomly generated. Previous work has demonstrated that the…
The chaotic spike train of a homoclinic dynamical system is self-synchronized by re-inserting a small fraction of the delayed output. Due to the sensitive nature of the homoclinic chaos to external perturbations, stabilization of very long…
The influence of oscillatory perturbations on autonomous strongly nonlinear systems in the plane is investigated. It is assumed that the intensity of perturbations decays with time, and their frequency increases according to a power law.…
This paper studies the problem of stabilization of a nonlinear system with time-varying delays in both sensing and actuation using event-triggered control. Our proposed strategy seeks to opportunistically minimize the number of control…
We present a systematic approach to reveal the correspondence between time delay dynamics and networks of coupled oscillators. After early demonstrations of the usefulness of spatio-temporal representations of time-delay system dynamics,…
We discuss some problems of dissipative chaos for open quantum systems in the framework of semiclassical and quantum distributions. For this goal, we propose a driven nonlinear oscillator with time-dependent coefficients, i.e. with…
We study the response of an ensemble of synchronized phase oscillators to an external harmonic perturbation applied to one of the oscillators. Our main goal is to relate the propagation of the perturbation signal to the structure of the…
The coupled electron-nuclear spin system in an InGaAs semiconductor as testbed of nonlinear dynamics can develop auto-oscillations, resembling time-crystalline behavior, when continuously excited by a circularly polarized laser. We expose…
Excitable systems with delayed feedback are important in areas from biology to neuroscience and optics. They sustain multistable pulsing regimes with different number of equidistant pulses in the feedback loop. Experimentally and…
The effect of multiplicative white noise on the resonance capture in non-isochronous systems with time-decaying pumping is investigated. It is assumed that the intensity of perturbations decays with time, and its frequency is asymptotically…