Noise-induced escape from bifurcating attractors: Symplectic approach in the weak-noise limit

Details Noise-induced escape from bifurcating attractors: Symplectic approach in the weak-noise limit Noise-induced escape from bifurcating attractors: Symplectic approach in the weak-noise limit

2009-08-04

arxiv.org/abs/0908.0465v1

Phys. Rev. E 80, 031147 (2009) [13 pages]

Physics

Condensed Matter

Statistical Mechanics

16 pages, 11 figures, submitted to Physical Review E

Scientific paper

10.1103/PhysRevE.80.031147

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.

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