title: Noise-induced escape from bifurcating attractors: Symplectic approach in the weak-noise limit.
abstract: The effect of noise is studied in one-dimensional maps undergoing transcritical, tangent, and pitchfork bifurcations. The attractors of the noiseless map become metastable states in the presence of noise. In the weak-noise limit, a symplectic two-dimensional map is associated with the original one-dimensional map. The consequences of their noninvertibility on the phase-space structures are discussed. Heteroclinic orbits are identified which play a key role in the determination of the escape rates from the metastable states. Near bifurcations, the critical slowing down justifies the use of a continuous-time approximation replacing maps by flows, which allows the analytic calculation of the escape rates. This method provides the universal scaling behavior of the escape rates at the bifurcations.
authors.affiliation: Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles, Code Postal 231, Campus Plaine, B-1050 Brussels, Belgium.
authors.forename: Jonathan
authors.initials: J
authors.lastname: Demaeyer
authors.forename: Pierre
authors.initials: P
authors.lastname: Gaspard