Fluctuation and Noise Letters Vol. 1, No. 1 (2001) L27–L33 c  World Scientific Publishing Company NOISE-INDUCED ESCAPE FROM THE LORENZ ATTRACTOR V.S. ANISHCHENKO, I.A. KHOVANOV, N.A. KHOVANOVA Physics Department, Saratov State University, Astrakhanskaya str. 83, 410026 Saratov, Russia wadim@chaos.ssu.runnet.ru, igor@chaos.ssu.runnet.ru, khovanova@chaos.ssu.runnet.ru D.G. LUCHINSKY, P.V.E. McCLINTOCK Department of Physics, Lancaster University, Lancaster, LA1 4YB, UK d.luchinsky@lancaster.ac.uk, p.v.e.mcclintock@lancaster.ac.uk Received 20 February 2001 Revised 14 March 2001 Accepted 20 March 2001 Noise-induced escape from a quasi-hyperbolic attractor in the Lorenz system is inves- tigated via an analysis of the distributions of both the escape trajectories and the cor- responding realizations of the random force. It is shown that a unique escape path exists, and that it consists of three parts with noise playing a different role in each. It is found that the mechanism of the escape from a quasi-hyperbolic attractor differs from that of escape from a non-hyperbolic attractor. The possibility of calculating the escape probability is discussed. Keywords : Noise-induced escape, quasi-hyperbolic attractor, non-equilibrium fluctua- tions, prehistory probability distribution 1. Introduction One of the longstanding unsolved problems in the theory of fluctuations is that of noise-induced escape from a chaotic attractor [1–3]. Chaotic systems are widespread in nature, and the study of their dynamics in the presence of noise is a topic of broad interdisciplinary interest whose potential applications include e.g. stabilization of the voltage standard [4] and laser systems [5], neuron dynamics [6], macromolecular transport in biological cells [7], and the control of migration in multistable systems [8–10]. The difficulty in solving the fluctuational escape problem stems largely from the fact that systems possessing strange attractors are far from thermal equilibrium: no general methods are available for estimation of the escape probabilities in such L27