Related papers: Order-by-disorder in classical oscillator systems
Effect of noise in inducing order on various chaotically evolving systems is reviewed, with special emphasis on systems consisting of coupled chaotic elements. In many situations it is observed that the uncoupled elements when driven by…
We consider a one-dimensional directional array of diffusively coupled oscillators. They are perturbed by the injection of a small additive noise, typically orders of magnitude smaller than the oscillation amplitude, and the system is…
The presence of noise in non linear dynamical systems can play a constructive role, increasing the degree of order and coherence or evoking improvements in the performance of the system. An example of this positive influence in a biological…
We have analyzed the interplay between noise and periodic spatial modulations in bistable systems outside equilibrium and found that noise is able to increase the spatial order of the system, giving rise to periodic patterns which otherwise…
The dynamics of an ensemble of bistable elements with global time-delayed coupling under the influence of noise is studied analytically and numerically. Depending on the noise level the system undergoes ordering transitions and demonstrates…
We study the noise effects in a driven system of globally coupled oscillators, with particular attention to the interplay between driving and noise. The self-consistency equation for the order parameter, which measures the collective…
We evoke the idea of representation of the chaotic attractor by the set of unstable periodic orbits and disclose a novel noise-induced ordering phenomenon. For long unstable periodic orbits forming the strange attractor the weights (or…
The effects of disorder in external forces on the dynamical behavior of coupled nonlinear oscillator networks are studied. When driven synchronously, i.e., all driving forces have the same phase, the networks display chaotic dynamics. We…
We study populations of oscillators, all-to-all coupled by means of quenched disordered phase shifts. While there is no traditional synchronization transition with a nonvanishing Kuramoto order parameter, the system demonstrates a specific…
Synchronization is a widespread phenomenon observed in physical, biological, and social networks, which persists even under the influence of strong noise. Previous research on oscillators subject to common noise has shown that noise can…
We analyze stability of a system which contains an harmonic oscillator non-linearly coupled to its second harmonic, in the presence of a driving force. It is found that there always exists a critical amplitude of the driving force above…
Theoretical models that describe oscillations in biological systems are often either a limit cycle oscillator, where the deterministic nonlinear dynamics gives sustained periodic oscillations, or a noise-induced oscillator, where a fixed…
We study synchronization of locally coupled noisy phase oscillators which move diffusively in a one-dimensional ring. Together with the disordered and the globally synchronized states, the system also exhibits several wave-like states which…
In this paper we present a general result with an easily checkable condition that ensures a transition from chaotic regime to regular regime in random dynamical systems with additive noise. We show how this result applies to a prototypical…
A solvable model of noise effects on globally coupled limit cycle oscillators is proposed. The oscillators are under the influence of independent and additive white Gaussian noise. The averaged motion equation of the system with infinitely…
We study synchronization and noise-induced resonance phenomena in systems of globally coupled oscillators, each possessing finite inertia. The behavior of the order parameter, which measures collective synchronization of the system, is…
Cooperative effects of periodic force and noise in globally Cooperative effects of periodic force and noise in globally coupled systems are studied using a nonlinear diffusion equation for the number density. The amplitude of the order…
Following the long-lived qualitative-dynamics tradition of explaining behavior in complex systems via the architecture of their attractors and basins, we investigate the patterns of switching between qualitatively distinct trajectories in a…
In nonlinear systems analysis, minor fractions of higher-order dynamics are often neglected for simplicity. Here, we show that machine epsilon levels of parasitic higher-order dynamics due to computer roundoff alone can cause divergence of…
We investigate an oscillator linearly coupled with a one-dimensional Ising system. The coupling gives rise to drastic changes both in the oscillator statics and dynamics. Firstly, there appears a second order phase transition, with the…