Enhancement of noise-induced escape through the existence of a chaotic saddle.

We study the noise-induced escape process in a prototype dissipative nonequilibrium system, the Ikeda map. In the presence of a chaotic saddle embedded in the basin of attraction of the metastable state, we find the novel phenomenon of a strong enhancement of noise-induced escape. This result is established by employing the theory of quasipotentials. Our finding is of general validity and should be experimentally observable.

[1]  Riccardo Mannella,et al.  Observation of saddle-point avoidance in noise-induced escape. , 1999 .

[2]  Robert Graham,et al.  Existence of a potential for dissipative dynamical systems , 1984 .

[3]  Kaufman,et al.  Kramers problem for a multiwell potential , 2000, Physical review letters.

[4]  Graham,et al.  Nonequilibrium potentials for dynamical systems with fractal attractors or repellers. , 1991, Physical review letters.

[5]  P. Hänggi,et al.  Discrete dynamics and metastability: Mean first passage times and escape rates , 1987 .

[6]  P. Hänggi,et al.  Reaction-rate theory: fifty years after Kramers , 1990 .

[7]  Beale.  Noise-induced escape from attractors in one-dimensional maps. , 1989, Physical review. A, General physics.

[8]  Peter Grassberger,et al.  Noise-induced escape from attractors , 1989 .

[9]  James A. Yorke,et al.  A procedure for finding numerical trajectories on chaotic saddles , 1989 .

[10]  Vadim N. Smelyanskiy,et al.  Fluctuations, Escape, and Nucleation in Driven Systems: Logarithmic Susceptibility , 1997 .

[11]  Esteve,et al.  Thermal Activation above a Dissipation Barrier: Switching of a Small Josephson Junction. , 1996, Physical review letters.

[12]  K. Ikeda.  Multiple-valued stationary state and its instability of the transmitted light by a ring cavity system , 1979 .

[13]  Graham,et al.  Nonequilibrium potential for coexisting attractors. , 1986, Physical review. A, General physics.

[14]  Y. Kifer.  Random Perturbations of Dynamical Systems , 1988 .

[15]  Vadim N. Smelyanskiy,et al.  Resonant directed diffusion in nonadiabatically driven systems , 1998 .

[16]  M. Freidlin,et al.  Random Perturbations of Dynamical Systems , 1984 .

[17]  V. I. Mel'Nikov,et al.  The Kramers problem : fifty years of development , 1991 .

[18]  S. Soskin.  Large Fluctuations in Multiattractor Systems and the Generalized Kramers Problem , 1999 .

[19]  D. Luchinsky,et al.  Corrals and Critical Behavior of the Distribution of Fluctuational Paths. , 1996, Physical review letters.

[20]  Mannella,et al.  Fluctuations and the energy-optimal control of chaos , 2000, Physical review letters.

[21]  Maier,et al.  Effect of focusing and caustics on exit phenomena in systems lacking detailed balance. , 1993, Physical review letters.

[22]  Lars Onsager,et al.  Fluctuations and Irreversible Processes , 1953 .

[23]  H. Kramers.  Brownian motion in a field of force and the diffusion model of chemical reactions , 1940 .

[24]  Lisa J. Lapidus,et al.  Stochastic Phase Switching of a Parametrically Driven Electron in a Penning Trap , 1999 .

[25]  Vadim Smelyanskiy,et al.  TIME OSCILLATIONS OF ESCAPE RATES IN PERIODICALLY DRIVEN SYSTEMS , 1999 .

[26]  P. Reimann,et al.  Escape rates for noisy maps with anomalous prefactors , 1996 .

[27]  C. Doering,et al.  Resonant activation over a fluctuating barrier. , 1992, Physical review letters.

[28]  C. Grebogi,et al.  Multistability and the control of complexity. , 1997, Chaos.

[29]  Christopher K. R. T. Jones,et al.  Global dynamical behavior of the optical field in a ring cavity , 1985 .

[30]  Mantegna,et al.  Noise enhanced stability in an unstable system. , 1996, Physical review letters.

[31]  Escape rates for noisy maps. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[32]  Maier,et al.  Transition-rate theory for nongradient drift fields. , 1992, Physical review letters.

[33]  Strong enhancement of noise-induced escape by nonadiabatic periodic driving due to transient chaos. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[34]  Zhukov,et al.  Dynamics of activated escape and its observation in a semiconductor laser , 2000, Physical review letters.

[35]  D. G. Luchinsky,et al.  Irreversibility of classical fluctuations studied in analogue electrical circuits , 1997, Nature.