噪声诱导的分岔吸引子逃逸：弱噪声极限下的辛方法
Noise-induced escape from bifurcating attractors: Symplectic approach in the weak-noise limit
摘要：
研究了噪声对一维映射的跨临界、切分叉和叉分叉的影响。无噪声映射的吸引子在噪声存在下变为亚稳态。在弱噪声极限下，一个辛二维映射与原来的一维映射相关联。的相空间结构上的不可逆性的后果进行了讨论。异宿轨道的确定起着关键的作用，在确定的逃逸率从亚稳态。在分叉附近，临界减速证明了使用连续时间近似代替地图的流动，这使得逃逸率的分析计算。该方法提供了逃逸率在分岔点处的普遍标度行为。
英文摘要：
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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