Physica D 181 (2003) 222–234 Noise-induced escape through a chaotic saddle: lowering of the activation energy Suso Kraut a,b,∗ , Ulrike Feudel b a Institut für Physik, Universität Potsdam, Postfach 601553, D-14415 Potsdam, Germany b ICBM, Carl von Ossietzky Universität, PF 2503, 26111 Oldenburg, Germany Received 19 December 2002; received in revised form 11 March 2003; accepted 21 March 2003 Communicated by R. Roy Abstract The noise-induced escape mechanism is investigated for a prototype time-discrete nonequilibrium system describing a laser in a ring cavity with optical feedback, the Ikeda map. For certain parameter values a chaotic saddle is embedded in the basin of attraction of the metastable state. This results in a lowering of the escape threshold for the activation energy, which is established by employing the theory of quasipotentials. Our findings are explained by the computation of the most probable exit path (MPEP), which lies partly on the chaotic saddle. The enhancement of escape turns out to be maximal if the MPEP lies entirely on the chaotic saddle. © 2003 Elsevier Science B.V. All rights reserved. PACS: 05.45.-a; 05.40.Ca; 05.70.Ln; 42.60.Mi Keywords: Chaotic saddle; Metastable; Activation energy 1. Introduction Noise-induced escape over a potential barrier has been studied extensively [1,2] since the seminal work by Kramers [3]. However, if the system under con- sideration is not in thermal equilibrium, as it was as- sumed in Kramers’ theory, many new features of the escape process can occur. Onsager and Machlup [4] realized that the escape process consists of large fluc- tuations, which are very rare, and that the trajectory peaks sharply around some optimal, i.e. most proba- ble escape path (MPEP). Thus, despite the stochastic ∗ Corresponding author. Present address: Institut für Physik, Uni- versität Potsdam, Postfach 601553, D-14415 Potsdam, Germany. Tel.: +49-3319771364; fax: +49-3319771142. E-mail address: suso@agnld.uni-potsdam.de (S. Kraut). nature of the escape process, the escape path is almost deterministic. Compared to the MPEP other paths have an exponentially smaller probability. That theory was derived for a small noise level σ → 0. In the last years, it has become possible to perform also experiments on the escape problem, which in- clude Josephson junctions [5], electronic circuits [6], optical traps [7], lasers [8,9], and an electron in a Pen- ning trap [10]. Some of the most interesting novel theoretical findings include an understanding of the singularities of the nonequilibrium potential [11–14], a pre-expo- nential factor of the Kramers rate [15], a symmetry breaking bifurcation of the MPEP [16] and a distri- bution of the escape paths originating from a cusp point singularity [17]. Although in general the escape 0167-2789/03/$ – see front matter © 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0167-2789(03)00098-8