延迟反馈的随机切换抑制基因调控系统中的振荡
Stochastic switching of delayed feedback suppresses oscillations in genetic regulatory systems
AI总结：
本文研究随机切换延迟对延迟反馈的影响，推导出快速切换极限下的有效延迟方程，并证明在基因调控模型中，两个振荡子系统间的快速切换可抑制振荡、实现稳定动力学。
摘要：
延迟和随机性在控制、物理和生物系统的数学描述中都是至关重要的成分。在本工作中，我们研究延迟中显式的动力学随机性如何调节延迟反馈的效应。为此，我们考虑一个混合模型，其中随机延迟由一个连续时间马尔可夫链演化，而在切换事件之间，所研究的系统通过一个确定性延迟方程演化。我们的主要贡献是在快速切换极限下计算出一个有效延迟方程。该有效方程保持了所有子系统延迟的影响，并且不能用单一的有效延迟来替代。为了说明这一计算的相关性，我们研究了一个受基因调控启发的随机切换延迟反馈的简单模型。我们表明，在两个振荡子系统之间足够快的切换可以产生稳定的动力学。
英文摘要：
Delays and stochasticity have both served as crucially valuable ingredients in mathematical descriptions of control, physical, and biological systems. In this work, we investigate how explicitly dynamical stochasticity in delays modulates the effect of delayed feedback. To do so, we consider a hybrid model where stochastic delays evolve by a continuous-time Markov chain, and between switching events, the system of interest evolves via a deterministic delay equation. Our main contribution is the calculation of an effective delay equation in the fast switching limit. This effective equation maintains the influence of all subsystem delays and cannot be replaced with a single effective delay. To illustrate the relevance of this calculation, we investigate a simple model of stochastically switching delayed feedback motivated by gene regulation. We show that sufficiently fast switching between two oscillatory subsystems can yield stable dynamics.
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