Noise Induced Escape from Different Types of Chaotic Attractor

Noise-induced escape from a quasi-attractor, and from the Lorenz attractor with non-fractal boundaries, are compared through measurements of optimal paths. It has been found that, for both types of attractor, there exists a most probable (optimal) escape trajectory, the prehistory of the escape being defined by the structure of the chaotic attractor. For a quasi-attractor the escape process is realized via several steps, which include transitions between low-period saddle cycles co-existing in the system phase space. The prehistory of escape from the Lorenz attractor is defined by stable and unstable manifolds of the saddle center point, and the escape itself consists of crossing the saddle cycle surrounding one of the stable point-attractors. A major unsolved problem in the theory of fluctuations is that of noise-induced escape from a chaotic attractor [1]. Chaotic systems are widespread in nature, and the study of their dynamics in the presence of fluctuations is both of fundamental interest, and also of importance in relation to a range of applications, e.g. to stabilization of the voltage standard [2], neuron dynamics [3], and laser systems [4]. The difficulty of solving the fluctuational escape problem stems largely from the fact that the dynamics of the system during large noise-induced deviations from deterministic chaotic trajectories remains obscure. In particular, it has been unclear whether or not there exists a unique optimal path along which escape from a chaotic attractor takes place. Theoretical predictions of the character of the optimal path distribution near a chaotic attractor do not yet exist. It has been established that fluctuational dynamics can be investigated directly through measurements of the so-called prehistory probability distribution of fluctuations [5,6], making it possible to examine situations for which the use of analytic methods still remains problematic. We have applied this technique to experimental investigations of noise-induced escape from a quasi-attractor and from the Lorenz attractor. CP502, Stochastic and Chaotic Dynamics in the Lakes: STOCHAOS, edited by D. S. Broomhead, E. A. Luchinskaya, P.V. E. McClintock, and T. Mullin © 2000 American Institute of Physics l-56396-915-7/00/$17.00