Sequential Noise-Induced Escapes for Oscillatory Network Dynamics
Sequential Noise-Induced Escapes for Oscillatory Network Dynamics
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DOI：
10.1137/17m1126412
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发表时间：
2018-01-01
影响因子：
2.1
通讯作者：
Ashwin, Peter
中科院分区：
文献类型：
--
作者：
Creaser, Jennifer;Tsaneva-Atanasova, Krasimira;Ashwin, Peter
众所周知，在多稳态系统中加入噪声会引起稳态之间的随机跃迁。跃迁的速率可以用无噪声系统的动力学和附加噪声来表征：对于存在渐近低噪声的潜在系统，著名的Kramers逃逸时间给出了平均逃逸时间的表达式。本文研究了网络中局部稳定吸引子和振荡吸引子之间的转换的一些一般性质和例子：每个节点的转换率可能会受到其他节点的动力学的影响。我们使用第一次通过时间理论来解释一些属性的缩放在文献中指出的一个理想化的模型，在小的系统中的癫痫发作的启动耦合hepatitis系统稳定和振荡吸引子。我们专注于连续逃逸的情况下，一个稳定的吸引子只是勉强稳定，但所有的节点开始在这种状态。当节点逃逸到振荡状态时，我们假设相比较而言，返回的过渡非常罕见。我们量化和表征所产生的序列的噪声引起的逃生。对于足够弱的耦合，我们表明，主方程的方法给出了一个很好的定量理解的顺序逃逸，但强耦合这种描述打破。
It is well known that the addition of noise in a multistable system can induce random transitions between stable states. The rate of transition can be characterized in terms of the noise-free system's dynamics and the added noise: for potential systems in the presence of asymptotically low noise the well-known Kramers' escape time gives an expression for the mean escape time. This paper examines some general properties and examples of transitions between local steady and oscillatory attractors within networks: the transition rates at each node may be affected by the dynamics at other nodes. We use first passage time theory to explain some properties of scalings noted in the literature for an idealized model of initiation of epileptic seizures in small systems of coupled bistable systems with both steady and oscillatory attractors. We focus on the case of sequential escapes where a steady attractor is only marginally stable but all nodes start in this state. As the nodes escape to the oscillatory regime, we assume that the transitions back are very infrequent in comparison. We quantify and characterize the resulting sequences of noise-induced escapes. For weak enough coupling we show that a master equation approach gives a good quantitative understanding of sequential escapes, but for strong coupling this description breaks down.