Noise-induced escape from bifurcating attractors: Symplectic approach in the weak-noise limit
arXiv:0908.0465 · doi:10.1103/PhysRevE.80.031147
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.
arXiv comment16 pages, 11 figures, submitted to Physical Review E
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