序贯逃逸：通过鞍形连接启动慢多米诺机制
Sequential escapes: onset of slow domino regime via a saddle connection
摘要：
我们探讨了耦合非线性系统在随机扰动影响下的序列逃逸行为。我们认为瞬态逃逸从一个稍微稳定的“静态”平衡到一个更稳定的“主动”平衡。耦合的存在引入了逃逸过程之间的依赖性：对于扩散耦合，存在强耦合极限（快多米诺制度），其中逃逸强烈同步，而对于没有部分逃逸稳定状态的中间耦合（慢多米诺制度），仍然存在延迟效应。这些制度可以与分叉的平衡在低噪声限制。在本文中，我们考虑了一个本地化的形式的非扩散（即脉冲状）耦合，并发现类似的变化与耦合强度的逃逸时间的分布。然而，我们发现过渡到一个缓慢的多米诺骨牌制度，是没有任何分叉的平衡。我们表明，这种转变可以理解为一个余维一鞍形连接分歧的低噪声限制。在过渡时，从一个吸引子的最可能的逃逸路径从另一个部分逃逸吸引子的盆击中逃逸鞍。在此分叉之后，我们发现后续逃逸时间的变异系数变异系数增加。
英文摘要：
We explore sequential escape behaviour of coupled bistable systems under the influence of stochastic perturbations. We consider transient escapes from a marginally stable "quiescent" equilibrium to a more stable "active" equilibrium. The presence of coupling introduces dependence between the escape processes: for diffusive coupling there is a strongly coupled limit (fast domino regime) where the escapes are strongly synchronised while for intermediate coupling (slow domino regime) without partially escaped stable states, there is still a delayed effect. These regimes can be associated with bifurcations of equilibria in the low-noise limit. In this paper we consider a localized form of non-diffusive (i.e pulse-like) coupling and find similar changes in the distribution of escape times with coupling strength. However we find transition to a slow domino regime that is not associated with any bifurcations of equilibria. We show that this transition can be understood as a codimension-one saddle connection bifurcation for the low-noise limit. At transition, the most likely escape path from one attractor hits the escape saddle from the basin of another partially escaped attractor. After this bifurcation we find increasing coefficient of variation of the subsequent escape times.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
