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arXiv · 0908.0465

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

Jonathan Demaeyer·Pierre Gaspard
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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.

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Jonathan Demaeyer, Pierre Gaspard. 2009-08-04. Noise-induced escape from bifurcating attractors: Symplectic approach in the weak-noise limit. https://doi.org/10.1103/physreve.80.031147

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