Zero-dispersion stochastic resonance (original) (raw)
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Stochastic resonance in underdamped, bistable systems
Physics Letters A, 2006
We carry out a detailed numerical investigation of stochastic resonance in underdamped systems in the non-perturbative regime. We point out that an important distinction between stochastic resonance in overdamped and underdamped systems lies in the lack of dependence of the amplitude of the noise-averaged trajectory on the noise strength, in the latter case. We provide qualitative explanations for the observed behavior and show that signatures such as the initial decay and long-time oscillatory behaviour of the temporal correlation function and peaks in the noise and phase averaged power spectral density, clearly indicate the manifestation of resonant behaviour in noisy, underdamped bistable systems in the weak to moderate noise regime.
Nonconventional stochastic resonance
Journal of Statistical Physics, 1993
It is argued, on the basis of linear response theory (LRT), that new types of stochastic resonance (SR) are to be anticipated in diverse systems, quite different from the one most commonly studied to date, which has a static double-well potential and is driven by a net force equal to the sum of periodic and stochastic terms. On this basis, three new nonconventional forms of SR are predicted, sought, found, and investigated both theoretically and by analogue electronic experiment: (a) in monostable systems; (b) in bistable systems with periodically modulated noise; and (c) in a system with coexisting periodic attractors. In each case, it is shown that LRT can provide a good quantitative description of the experimental results for sufficiently weak driving fields. It is concluded that SR is a much more general phenomenon than has hitherto been appreciated.
A new perspective on stochastic resonance in monostable systems
New Journal of Physics, 2010
Stochastic resonance induced by multiplicative white noise is theoretically studied in forced damped monostable oscillators. A stochastic amplitude equation is derived for the oscillation envelope, which has a linear stochastic resonance. This phenomenon is persistent when nonlinearities are considered. We propose three simple systems-a horizontally driven pendulum, a forced electrical circuit and a laser with an injected signal-that display this stochastic resonance. References 12
Two-State Theory of Nonlinear Stochastic Resonance
Physical Review Letters, 2003
An amenable, analytical two-state description of the nonlinear population dynamics of a noisy bistable system driven by a rectangular subthreshold signal is put forward. Explicit expressions for the driven population dynamics, the correlation function (its coherent and incoherent part), the signal-to-noise ratio (SNR) and the Stochastic Resonance (SR) gain are obtained. Within a suitably chosen range of parameter values this reduced description yields anomalous SR-gains exceeding unity and, simultaneously, gives rise to a non-monotonic behavior of the SNR vs. the noise strength. The analytical results agree well with those obtained from numerical solutions of the Langevin equation.
Physical review. E, Statistical, nonlinear, and soft matter physics, 2003
The method of moments is applied to an underdamped bistable oscillator driven by Gaussian white noise and a weak periodic force for the observations of stochastic resonance and the resulting resonant structures are compared with those from Langevin simulation. The physical mechanisms of the stochastic resonance are explained based on the evolution of the intrawell frequency peak and the above-barrier frequency peak via the noise intensity and the fluctuation-dissipation theorem, and the three possible sources of stochastic resonance in the system are confirmed. Additionally, with the noise intensity fixed, the stochastic resonant structures are also observed by adjusting the nonlinear parameter.
Stochastic Resonance in coupled Underdamped Bistable Systems, Phys Rev E 82, 046224 (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
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 without external periodic force
Physical Review Letters, 1993
A model of a two-dimensional autonomous system subject to external noise is investigated. Without noise the system has a stable limit cycle in a certain region of control parameter. Various noise-induced eAects have been found numerically, such as a noise-induced frequency shift in the presence of the deterministic limit cycle, and noise-induced coherent oscillations in the absence of the deterministic limit cycle. An interesting result is that the stochastic resonance phenomenon appears in a system without an external signal and when the asymptotic state of the deterministic system is stationary.
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.