Related papers: Separatrix crossing due to multiplicative colored …
We consider the simulation of interacting high-dimensional systems using pairwise interacting qubits. The main tool in this context is the generation of effective many-body interactions, and we examine a number of different protocols for…
Nonlinear dynamical systems are sometimes under the influence of random fluctuations. It is desirable to examine possible bifurcations for stochastic dynamical systems when a parameter varies. A computational analysis is conducted to…
We experimentally demonstrate a new class of optomechanical nonlinearities in weakly damped micromechanical resonators, arising from the interplay between the Duffing nonlinearity, intermodal coupling, and thermal fluctuations. Within the…
We consider a quantum two-level system perturbed by classical noise. The noise is implemented as a stationary diffusion process in the off-diagonal matrix elements of the Hamiltonian, representing a transverse magnetic field. We determine…
Fluctuational transitions between two co-existing chaotic attractors, separated by a fractal basin boundary, are studied in a discrete dynamical system. It is shown that the mechanism for such transitions is determined by a hierarchy of…
We investigate the effects of exponentially correlated noise on birhythmic van der Pol type oscillators. The analytical results are obtained applying the quasi-harmonic assumption to the Langevin equation to derive an approximated…
We analyze theoretically and experimentally the influence of current noise on the longitudinal mode hopping dynamics of a bulk semiconductor laser. It is shown that the mean residence times on each mode have different sensitivity to…
The effects of noise on the dynamics of nonlinear systems is known to lead to many counter-intuitive behaviors. Using simple planar limit cycle oscillators, we show that the addition of moderate noise leads to qualitatively different…
We present a picture of phase transitions of the system with colored multiplicative noise. Considering the noise amplitude as the power-law dependence of the stochastic variable $x^a$ we show the way to phase transitions disorder-order and…
We consider a white noise perturbation of dynamics in the neighborhood of a heteroclinic network. We show that under the logarithmic time rescaling the diffusion converges in distributon in a special topology to a piecewise constant process…
Dichotomous noise appears in a wide variety of physical and mathematical models. It has escaped attention that the standard results for the long time properties cannot be applied when unstable fixed points are crossed in the asymptotic…
This paper presents a heuristic derivation of a geometric minimum action method that can be used to determine most-probable transition paths in noise-driven dynamical systems. Particular attention is focused on systems that violate detailed…
We study the trajectories followed by a particle subjected to weak noise when escaping from the domain of attraction of a stable fixed point. If detailed balance is absent, a _focus_ may occur along the most probable exit path, leading to a…
We developed a powerful computational approach to elaborate on onset mechanisms of deterministic chaos due to complex homoclinic bifurcations in diverse systems. Its core is the reduction of phase space dynamics to symbolic binary…
We investigate dynamically and statistically diffusive motion in a chain of linearly coupled 2-dimensional symplectic McMillan maps and find evidence of subdiffusion in weakly and strongly chaotic regimes when all maps of the chain possess…
Noise has significant impact on nonlinear phenomena. Here we demonstrate that, in opposition to previous assumptions, additive noise interfere with the linear stability of scalar nonlinear systems when these are subject to time delay. We…
In this set of lectures, we review briefly some of the recent developments in the study of the chaotic dynamics of nonlinear oscillators, particularly of damped and driven type. By taking a representative set of examples such as the…
We study the statistical properties of overdamped particles driven by two cross-correlated multiplicative Gaussian white noises in a time-dependent environment. Using the Langevin and Fokker-Planck approaches, we derive the exact…
It is known that a linear hamiltonian system has too many invariant measures, thus the problem of convergence to Gibbs measure has no sense. We consider linear hamiltonian systems of arbitrary finite dimension and prove that, under the…
The influence of multiplicative white noise on the resonance capture of strongly nonlinear oscillatory systems under chirped-frequency excitations is investigated. It is assumed that the intensity of the perturbation decays polynomially…