A variational method for analyzing limit cycle oscillations in stochastic hybrid systems
A variational method for analyzing limit cycle oscillations in stochastic hybrid systems
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DOI：
10.1063/1.5027077
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发表时间：
2018-06-01
期刊：
影响因子：
2.9
通讯作者：
MacLaurin, James
中科院分区：
文献类型：
--
作者：
Bressloff, Paul C.;MacLaurin, James
生物学中的许多系统都可以用分段连续的常微分方程组来建模，并根据一个被称为随机混合系统或分段确定性马尔可夫过程(PDMP)的马尔可夫跳跃过程在不同状态之间切换。在快速切换极限下，动态收敛到一个确定性的微分方程组。在这篇文章中，我们发展了一种随机混合系统的相位归约方法，该系统在确定性极限下支持一个稳定的极限环。一个经典的例子是神经元的Morris-LeCar模型，其中切换的马尔可夫过程是开放的离子通道的数量，连续的过程是膜电压。我们概述了相减的变分原理，给出了由此产生的相动力学的精确解析表达式。我们证明了这种分解在时间尺度上是准确的，该时间尺度在转换率为(-1)的元素中是指数的。也就是说，我们证明了对于常数C，离开极限环的O(A)邻域的期望时间小于T标度的概率为Texp(-Ca/是的元素)。由AIP出版公司出版。
Many systems in biology can be modeled through ordinary differential equations, which are piecewise continuous, and switch between different states according to a Markov jump process known as a stochastic hybrid system or piecewise deterministic Markov process (PDMP). In the fast switching limit, the dynamics converges to a deterministic ODE. In this paper, we develop a phase reduction method for stochastic hybrid systems that support a stable limit cycle in the deterministic limit. A classic example is the Morris-Lecar model of a neuron, where the switching Markov process is the number of open ion channels and the continuous process is the membrane voltage. We outline a variational principle for the phase reduction, yielding an exact analytic expression for the resulting phase dynamics. We demonstrate that this decomposition is accurate over timescales that are exponential in the switching rate is an element of(-1). That is, we show that for a constant C, the probability that the expected time to leave an O(a) neighborhood of the limit cycle is less than T scales as Texp (-Ca/is an element of). Published by AIP Publishing.