Analysis of synchronization of chaotic systems by noise: An experimental study

Abstract

The behavior of uncoupled chaotic systems under the influence of external noise has been the subject of recent work. Some of these studies claim that chaotic systems driven by the same noise do synchronize, while other studies contradict this conclusion. In this work we have undertaken an experimental study of the effect of noise on identically driven analog circuits. The main conclusion is that synchronization is induced by a nonzero mean of the signal and not by its stochastic character. ͓S1063-651X͑97͒09310-0͔PACS number͑s͒: 05.45.ϩb, 05.40.ϩj, 84.30.Bv

Synchronization of chaotic maps by symmetric common noise

“…It was pointed out that the origin of nonchaotic behavior is that the Lorenz system driven by large enough constant perturbations is actually stable at the fixed points [5,7]. Very recently, Sanchez et al [8] analyzed the synchronization of chaotic systems by noise in an experiment with the Chua circuit, again drawing the conclusion that synchronization may be achieved only by biased noise, and not symmetric noise.So it seems that symmetric noise cannot convert a chaotic system into a nonchaotic one, so that synchronization will occur for systems in common noise. In this letter, we are going to present an example that synchronization can actually be achieved by symmetric, zero-mean common noise.…”

“…Synchronization with λ < 0 occurs for σ 2 > 0.24. So, in contrast to the examples in [1][2][3][4][5][6][7][8], the sensitivity of this chaotic map can be suppressed by zero-mean noise, so that systems starting from different initial conditions will finally collapse into the same final orbit.The synchronization can be understood from the view point of the convergence region of the map. We perform two calculations: one is the distribution of the state of the system; and the other the distribution of the finite-time Lyapunov exponents defined as[5]…”

Spatiotemporal order out of noise

“…First the phenomenon was considered an artifact arising from a finite precision in numerical simulations ͑Pik-ovsky, 1994͒. Later it was attributed to a nonzero mean value of the noisy signal ͑Herzel and Freund, 1995;Malescio, 1996;Sánchez et al, 1997͒. More recently it has been demonstrated for zero-mean, additive Gaussian white noises of large enough intensity in certain chaotic maps ͑Lai and Zou, 1998; Toral et al, 2001͒ ͓the case with parametric noise was considered by Minai and Anand ͑1998͔͒. The generalization to the weaker level of phase synchronization was considered in the case of two nonidentical chaotic systems under common noise by Zhou and Kurths ͑2002a͒, and experimentally observed in noisy-neuronal oscillators by Neiman and Russell ͑2002͒.…”

Synchronization of chaotic systems by common random forcing

“…The introduction of a non-zero mean noise means that we are altering essentially the properties of the deterministic map. Noise induced synchronization has been since studied for other chaotic systems such as the Lorenz model [1,2] and the Chua circuit [3,5]. Synchronization of trajectories starting with different initial conditions but using otherwise the same sequence of random numbers was observed in the numerical integration of a Lorenz system in the presence of a noise distributed uniformly in the interval [0, W L ], i.e.…”

“…The issue of whether chaotic systems can be synchronized by common random noise sources has attracted much attention recently [1][2][3][4][5][6]. It has been reported that for some chaotic maps, the introduction of the same (additive) noise in independent copies of the same map could lead (for large enough noise intensity) to a collapse onto the same trajectory, independently of the initial condition assigned to each of the copies [1].…”