论文标题
随机性在噪声引起的临界点级联反应中的作用：主方程方法
The Role of Stochasticity in Noise-Induced Tipping Point Cascades: A Master Equation Approach
论文作者
论文摘要
在模型和经验中，在一系列物理和生物系统中，临界点已经无处不在。研究如何通过系统级联级联的问题进行了很好的研究，这是一个重要的问题。尤其是对噪声引起的小费的研究可以为小费级联提供关键的见解。在这里，我们考虑了一个简单的模型系统的特定示例，该系统可能具有级联的临界点。该模型由两个具有潜在地位效应和随机动力学的相互作用种群组成，在通过分散连接的单独斑块中，可以产生双重性。从生态学的角度来看，我们寻找救援效应，其中一个人口可以防止第二人口崩溃。作为研究随机动力学的一种方式，我们使用植根于化学反应网络理论的基于个体的建模方法。然后，使用连续的马尔可夫链和第一次通行时间的理论，我们本质上是通过只有四个状态的马尔可夫链的原始高维模型近似或模仿原始的高维模型，每个状态都对应于种群阈值的组合。对该简化模型的分析表明，何时可能恢复系统，以及在整个系统中倾斜级联时。
Tipping points have been shown to be ubiquitous, both in models and empirically in a range of physical and biological systems. The question of how tipping points cascade through systems has been less well studied and is an important one. A study of noise-induced tipping, in particular, could provide key insights into tipping cascades. Here, we consider a specific example of a simple model system that could have cascading tipping points. This model consists of two interacting populations with underlying Allee effects and stochastic dynamics, in separate patches connected by dispersal, which can generate bistability. From an ecological standpoint, we look for rescue effects whereby one population can prevent the collapse of a second population. As a way to investigate the stochastic dynamics, we use an individual-based modeling approach rooted in chemical reaction network theory. Then, using continuous-time Markov chains and the theory of first passage times, we essentially approximate, or emulate, the original high-dimensional model by a Markov chain with just four states, where each state corresponds to a combination of population thresholds. Analysis of this reduced model shows when the system is likely to recover, as well as when tipping cascades through the whole system.
