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We consider classical nonlinear oscillators on hexagonal lattices. When the coupling between the elements is repulsive, we observe coexisting states, each one with its own basin of attraction. These states differ by their degree of…
Under general conditions imposed on an active stochastic oscillator, we study change in the size and shape of its average limit cycle as a function of temperature. Such dynamics occur in a multitude of nonequilibrium systems, including the…
Experimental study on noise-induced synchronization of crystal oscillators is presented. Two types of circuits were constructed: one consists of two Pierce oscillators that were isolated from each other and received a common noise input,…
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…
We consider a system of globally-coupled phase-only oscillators with distributed intrinsic frequencies and evolving in presence of distributed Gaussian, white noise, namely, a Gaussian, white noise whose strength for every oscillator is a…
The synchronized phase of globally coupled nonlinear oscillators subject to noise fluctuations is studied by means of a new analytical approach able to tackle general couplings, nonlinearities, and noise temporal correlations. Our results…
We consider effect of stochastic sources upon self-organization process being initiated with creation of the limit cycle. General expressions obtained are applied to the stochastic Lorenz system to show that departure from equilibrium…
A universal mechanism underlying generalized synchronization conditions in unidirectionally coupled stochastic oscillators is considered. The consideration is carried out in the framework of a modified system with additional dissipation.…
We present recent results on noise-induced transitions in a nonlinear oscillator with randomly modulated frequency. The presence of stochastic perturbations drastically alters the dynamical behaviour of the oscillator: noise can wash out a…
After decades of study, there are only two known mechanisms to induce global synchronization in a population of oscillators: deterministic coupling and common forcing. The inclusion of independent random forcing in these models typically…
Experimental realization and quantitative investigation of common-noise-induced synchronization of limit-cycle oscillations subject to random telegraph signals are performed using an electronic oscillator circuit. Based on our previous…
We study a model consisting of $N$ nonlinear oscillators with {\em global periodic} coupling and {\em local multiplicative} and additive noises. The model was shown to undergo a nonequilibrium phase transition towards a broken-symmetry…
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…
We study phase entrainment of Kuramoto oscillators under different conditions on the interaction range and the natural frequencies. In the first part the oscillators are entrained by a pacemaker acting like an impurity or a defect. We…
We study the effects of noise on the collective dynamics of an ensemble of coupled phase oscillators whose natural frequencies are all identical, but whose coupling strengths are not the same all over the ensemble. The intensity of noise…
We report on nonequilibrium interaction phenomena between adjacent but electrostatically separated nanostructures in GaAs. A current flowing in one externally biased nanostructure causes an excitation of electrons in a circuit of a second…
Inspired by the observation of a distributed time delay in the nonlinear response of an optical resonator, we investigate the effects of a similar delay on a noise-driven mechanical oscillator. For a delay time that is commensurate with the…
Many networks must maintain synchrony despite the fact that they operate in noisy environments. Important examples are stochastic inertial oscillators, which are known to exhibit fluctuations with broad tails in many applications, including…
A system of four coupled oscillators that exhibits unusual synchronization phenomena has been ana- lyzed. Existence of a one-way heteroclinic network, called heteroclinic ratchet, gives rise to uni-directional (de)synchronization between…
We examine the design of the entrainment process for an uncountably infinite collection of coupled phase oscillators that are all subject to the same periodic driving signal. In the absence of coupling, an appropriately designed input can…