Stochastic resonance in chaotic systems (original) (raw)

Stochastic resonance in deterministic chaotic systems The mechanism of stochastic resonance

A Crisanti, M Falcioni, G Lacorata et al. Predictability of velocity and temperature fields in intermittent turbulence A Crisanti, M H Jensen, G Paladin et al. Stochastic resonance: noise-enhanced order Vadim S Anishchenko, Arkady B Neiman, F Moss et al. Predictability in spatially extended systems G Paladin and A Vulpiani Regular and chaotic motion of fluid particles in a two-dimensional fluid M Falcioni, G Paladin and A Vulpiani Analogue studies of nonlinear systems D G Luchinsky, P V E McClintock and M I Dykman Fractal measures in the random-field Ising model S N Evangelou The mechanism of stochastic resonance R Benzi, A Sutera and A Vulpiani Characterisation of intermittency in chaotic systems R Benzi, G Paladin, G Parisi et al. Abstract. We propose a mechanism which produces periodic variarions of the degree of prediaability in dynamical systems. It is shown that even in the absence of noise when the control parameter changes periodically in time, below and above the m o l d for the onset of chaos, stochastic resonance effects appear. As a result one has an alternation of chaotic and regular. i.e. predictable, evolutions in m dmst periodic way, so that the Lyapnnov exponent is positive but some time correlations do not d a y .

Stochastic resonance in deterministic chaotic systems

Journal of Physics A: Mathematical and General, 1994

We propose a mechanism which produces periodic variations of the degree of predictability in dynamical systems. It is shown that even in the absence of noise when the control parameter changes periodically in time, below and above the threshold for the onset of chaos, stochastic resonance effects appears. As a result one has an alternation of chaotic and regular, i.e. predictable, evolutions in an almost periodic way, so that the Lyapunov exponent is positive but some time correlations do not decay.

Stochastic Resonance in Chaotic Dynamics

It is suggested that chaotic dynamical systems characterized by intermittent jumps between two preferred regions of phase space display an enhanced sensitivity to weak periodic forcings through a stochastic resonance-like mechanism. This possibility is illustrated by the study of the residence time distribution in two examples of bi-modal chaos: the periodically forced Duffing oscillator and a 1-dimensional map showing intermittent behavior.

Stochastic resonance in a bistable system driven by a chaotic signal

Technical Physics Letters, 2006

The behavior of a bistable oscillator under the action of a chaotic signal from a Rössler oscillator with a spiral attractor is considered. The influence of the width of the main spectral line of the chaotic drive signal on the signal to noise ratio at the response system's output has been studied.

Chaotic resonance: A simulation

Journal of Statistical Physics, 1993

Stochastic resonance is a statistical phenomenon that has been observed in periodically modulated, noise-driven, bistable systems. The characteristic signatures of the effect include an increase in the signal-to-noise of the output as noise is added to the system, and exponentially decreasing peaks in the probability density as a function of residence times in one state. Presented are the results of a numerical simulation where these same signatures were observed by adding a chaotic driving term instead of a white noise term. Although the probability distributions of the noise and chaos inputs were significantly different, the stochastic and chaotic resonances were equal within the experimental error.

Stochastic resonance and chaotic resonance in bimodal maps: A case study

Pramana-journal of Physics, 2002

We present the results of an extensive numerical study on the phenomenon of stochastic resonance in a bimodal cubic map. Both Gaussian random noise as well as deterministic chaos are used as input to drive the system between the basins. Our main result is that when two identical systems capable of stochastic resonance are coupled, the SNR of either system is enhanced at an optimum coupling strength. Our results may be relevant for the study of stochastic resonance in biological systems.

Experimental study of stochastic resonance in a Chua’s circuit operating in a chaotic regime

2006

We present results of an experimental study of stochastic resonance in an electronic Chua's circuit whose dynamics switches between two different stable chaotic attractors when it is driven by a periodic signal and a Gaussian white noise. Due to the internal dynamics of the attractors the minimum amplitude for the external forcing to induce jumps strongly depends on the external frequency.

Resonant phenomena in extended chaotic systems subject to external noise: The Lorenz'96 model case

Physica a-Statistical Mechanics and Its Applications, 2008

We investigate the effects of a time-correlated noise on an extended chaotic system. The chosen model is the Lorenz'96, a kind of "toy" model used for climate studies. Through the analysis of the system's time evolution and its time and space correlations, we have obtained numerical evidence for two stochastic resonance-like behavior. Such behavior is seen when both, the usual and a generalized signal-to-noise ratio function are depicted as a function of the external noise intensity or the system size. The underlying mechanism seems to be associated to a noise-induced chaos reduction. The possible relevance of these and other findings for an optimal climate prediction are discussed.

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