相关论文: Effects of moderate noise on a limit cycle oscilla…
Additive noise is known to produce counter-intuitive behaviors in nonlinear dynamical systems. Previously, it was shown that systems with a deterministic limit cycle can display bistable switching between metastable states in the presence…
Nonlinear oscillators are a key modelling tool in many applications. The influence of annealed noise on nonlinear oscillators has been studied intensively. It can induce effects in nonlinear oscillators not present in the deterministic…
Fluctuations and noise may alter the behavior of dynamical systems considerably. For example, oscillations may be sustained by demographic fluctuations in biological systems where a stable fixed point is found in the absence of noise. We…
The effect of small-amplitude noise on excitable systems with large time-scale separation is analyzed. It is found that small random perturbations of the fast excitatory variable result in the onset of a quasi-deterministic limit cycle…
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 consider a stochastic perturbation of a FitzHugh-Nagumo system. We show that it is possible to generate oscillations for values of parameters which do not allow oscillations for the deterministic system. We also study the appearance of a…
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…
An experimental arrangement and a set of experiments are developed to generate empirical evidence of the effect of noise on a rotating, macro-scale cantilever structure. The experiment is a controlled representation of a rotating machinery…
Complex dynamical systems may exhibit multiple steady states, including time-periodic limit cycles, where the final trajectory depends on initial conditions. With tuning of parameters, limit cycles can proliferate or merge at an exceptional…
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 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…
We study the effect of additive Brownian noise on an ODE system that has a stable hyperbolic limit cycle, for initial data that are attracted to the limit cycle. The analysis is performed in the limit of small noise - that is, we modulate…
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…
We treat analytically a model that captures several features of the phenomenon of spatially inhomogeneous reversal of an order parameter. The model is a classical Ginzburg-Landau field theory restricted to a bounded one-dimensional spatial…
Positive feedback and cooperativity in the regulation of gene expression are generally considered to be necessary for obtaining bistable expression states. Recently, a novel mechanism of bistability termed emergent bistability has been…
Transient properties of different physical systems with metastable states perturbed by external white noise have been investigated. Two noise-induced phenomena, namely the noise enhanced stability and the resonant activation, are…
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…
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…
We analyze a piecewise-linear FitzHugh-Nagumo model. The system exhibits a canard near which both small amplitude and large amplitude periodic orbits exist. The addition of small noise induces mixed-mode oscillations (MMOs) in the vicinity…
We investigate feedback control of the cooperative dynamics of two coupled neural oscillators that is induced merely by external noise. The interacting neurons are modelled as FitzHugh-Nagumo systems with parameter values at which no…