Stochastic resonance in two coupled bistable systems (original) (raw)

Stochastic Resonance in two Coupled Underdamped Bistable Systems

We consider a system of two coupled bistable systems driven by both periodic and noise sources, focusing mainly on stochastic resonance (SR). In the absence of coupling, we found two critical damping parameters: one for the onset of resonances, and another for which theses resonances are optimum. We demonstrate that the absence of resonances in the weak coupling regime, is solely due to the presence of chaos in the system. Turning on the coupling, we found that the strong coupling regime induces a coherence that manifests itself by the matching of the signal to noise ratios of both subsystems. Finally, we demonstrate that our system does not synchronize for any coupling parameter.

Stochastic resonance in coupled underdamped bistable systems

Physical Review E, 2010

We study onset and control of stochastic resonance ͑SR͒ phenomenon in two driven bistable systems, mutually coupled and subjected to independent noises, taking into account the influence of both the inertia and the coupling. In the absence of coupling, we found two critical damping parameters: one for the onset of SR and another for which SR is optimum. We then show that in weakly coupled systems, emergence of SR is governed by chaos. A strong coupling between the two oscillators induces coherence in the system; however, the systems do not synchronize no matter what the coupling is. Moreover, a specific coupling parameter is found for which the SR of each subsystem is optimum. Finally, a scheme for controlling SR in such coupled systems is proposed by introducing a phase difference between the two coherent driving forces.

Stochastic Resonance in coupled Underdamped Bistable Systems, Phys Rev E 82, 046224 (2010)

Stochastic resonance in a locally excited system of bistable oscillators

The European Physical Journal B, 2011

Stochastic resonance is studied in a one-dimensional array of overdamped bistable oscillators in the presence of a local subthreshold periodic perturbation. The system can be treated as an ensemble of pseudospins tending to align parallel which are driven dynamically by an external periodic magnetic field. The oscillators are subjected to a dynamic white noise as well as to a static topological disorder. The latter is quantified by the fraction of randomly added long-range connections among ensemble elements. In the low connectivity regime the system displays an optimal global stochastic resonance response if a small-world network is formed. In the mean-field regime we explain strong changes in the dynamic disorder strength provoking a maximal stochastic resonance response via the variation of fraction of long-range connections by taking into account the ferromagnetic-paramagnetic phase transition of the pseudospins. The system size analysis shows only quantitative power-law type changes on increasing number of pseudospins.

Stochastic resonance in finite arrays of bistable elements with local coupling

European Physical Journal B, 2009

In this article, we investigate the stochastic resonance (SR) effect in a finite array of noisy bistable systems with nearest-neighbor coupling driven by a weak time-periodic driving force. The array is characterized by a collective variable. By means of numerical simulations, the signal-to-noise ratio (SNR) and the gain are estimated as functions of the noise and the interaction coupling strength. A strong enhancement of the SR phenomenon for this collective variable in comparison with SR in single unit bistable systems is observed. Gains larger than unity are obtained for some parameter values and multi-frequency driving forces, indicating that the system is operating in a non-linear regime albeit the smallness of the driving amplitude. The large SNR values observed are basically due to the fact that the output fluctuations are small and short lived, in comparison with their typical values in a linear regime. A non-monotonic behavior of the SNR with the coupling strength is also obtained.

Synchronization effects in networks of stochastic bistable oscillators

Mathematics and Computers in Simulation, 2002

We study the collective dynamics of one-and two-dimensional lattices of coupled stochastic, non-homogeneous oscillators in terms of synchronization. This phenomenon manifests itself as an entrainment of the mean switching frequencies in the form of frequency-locking and frozen synchronized states and as in-or anti-phase hopping dynamics. We analyze the conditions for the onset and existence of these different behavioral regimes.

Role of fluctuations in the response of coupled bistable units to weak time-periodic driving forces

Physical Review E, 2008

We analyze the stochastic response of a finite set of globally coupled noisy bistable units driven by rather weak time-periodic forces. We focus on the stochastic resonance and phase frequency synchronization of the collective variable, defined as the arithmetic mean of the variable characterizing each element of the array. For single-unit systems, stochastic resonance can be understood with the powerful tools of linear response theory. Proper noise-induced phase frequency synchronization for a single-unit system in this linear response regime does not exist. For coupled arrays, our numerical simulations indicate an enhancement of the stochastic resonance effects leading to gains larger than unity as well as genuine phase frequency synchronization. The nonmonotonicity of the response with the strength of the coupling strength is investigated. Comparison with simplifying schemes proposed in the literature to describe the random response of the collective variable is carried out.

Stochastic resonance in bistable systems driven by harmonic noise

Physical review letters, 1994

We study stochastic resonance in a bistable system which is excited simultaneously by white and harmonic noise which we understand as the signal. In our case the spectral line of the signal has a nite width as it occurs in many real situations. Using techniques of cumulant analysis as well as computer simulations we nd that the e ect of stochastic resonance is preserved in the case of harmonic noise excitation. Moreover we show that the width of the spectral line of the signal at the output can be decreased via stochastic resonace. The last could be of importance in the practical using of the stochastic resonance. PACS number(s): 05.40.+j, 02.50.+s Typeset using REVT E X

Frequency-sensitive stochastic resonance in periodically forced and globally coupled systems

The European Physical Journal B, 1998

A model of globally coupled bistable systems consisting of two kinds of sites, subject to periodic driving and spatially uncorrelated stochastic force, is investigated. The extended system models the competing process of activators and suppressers. Analytical computations for linear response of the system to the external periodic forcing is carried out. Noise-induced Hopf bifurcation is revealed, and stochastic resonance, sensitively depending on the frequency of the external forcing, is predicted under the Hopf bifurcation condition. Numerical simulations agree with the analytical predictions satisfactorily.

Synchronization of noisy systems by stochastic signals

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 1999

We study, in terms of synchronization, the nonlinear response of noisy bistable systems to a stochastic external signal, represented by Markovian dichotomic noise. We propose a general kinetic model which allows us to conduct a full analytical study of the nonlinear response, including the calculation of cross-correlation measures, the mean switching frequency, and synchronization regions. Theoretical results are compared with numerical simulations of a noisy overdamped bistable oscillator. We show that dichotomic noise can instantaneously synchronize the switching process of the system. We also show that synchronization is most pronounced at an optimal noise level-this effect connects this phenomenon with aperiodic stochastic resonance. Similar synchronization effects are observed for a stochastic neuron model stimulated by a stochastic spike train.

Stochastic resonance in two coupled bistable systems (original) (raw)

Related papers