瞬态网络动力学中的快多米诺和慢多米诺机制
Fast and slow domino regimes in transient network dynamics
摘要：
众所周知，在多稳态动力系统中加入噪声会引起从一个稳定状态到另一个稳定状态的随机跃迁。对于低噪声，跃迁之间的时间具有指数尾，Kramers公式给出了渐近极限中的平均逃逸时间的表达式。如果多个多稳态系统耦合成一个网络结构，一个点的跃迁可能会改变其他点的跃迁性质。我们研究了从“静态”吸引子逃逸到“活动”吸引子的情况，其中可以忽略返回的转换。根据耦合强度的不同，有不同性质的过渡区。对于小耦合强度的过渡率简单地修改，但过渡仍然是随机的。对于大的耦合强度，转换大约同步发生-我们称之为“快速多米诺骨牌”制度。还有一个中间耦合机制，一些转变无情地发生，但延迟可能是任意长的-我们称之为“慢多米诺骨牌”机制。我们在低噪声限制的条件下，这些制度的潜在景观的耦合系统的分叉。我们展示了耦合的时间分布和（一般）的逃逸序列的系统上的效果。
英文摘要：
It is well known that the addition of noise to a multistable dynamical system can induce random transitions from one stable state to another. For low noise, the times between transitions have an exponential tail and Kramers' formula gives an expression for the mean escape time in the asymptotic limit. If a number of multistable systems are coupled into a network structure, a transition at one site may change the transition properties at other sites. We study the case of escape from a "quiescent" attractor to an "active" attractor in which transitions back can be ignored. There are qualitatively different regimes of transition, depending on coupling strength. For small coupling strengths the transition rates are simply modified but the transitions remain stochastic. For large coupling strengths transitions happen approximately in synchrony - we call this a "fast domino" regime. There is also an intermediate coupling regime some transitions happen inexorably but with a delay that may be arbitrarily long - we call this a "slow domino" regime. We characterise these regimes in the low noise limit in terms of bifurcations of the potential landscape of a coupled system. We demonstrate the effect of the coupling on the distribution of timings and (in general) the sequences of escapes of the system.
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