复杂动力系统的稳定性阈值方法
Stability threshold approach for complex dynamical systems
摘要：
提出了一种新的度量复杂动力系统对大扰动稳定性的方法--稳定性阈值。它量化了能够破坏系统并将其切换到不期望的动态状态的最弱扰动的大小。在相空间中，稳定性阈值对应于“最薄的网站”的吸引盆地，因此表示最“危险”的扰动方向。我们引入了一个计算算法的稳定性阈值的量化，并证明所提出的方法是有效的，并提供了重要的见解。所获得的结果的一般性定义了它们在工程，神经科学，电网，地球科学等领域的应用的巨大潜力和许多其他复杂系统的鲁棒性进行了研究。
英文摘要：
A new measure to characterize stability of complex dynamical systems against large perturbation is suggested, the stability threshold (ST). It quantifies the magnitude of the weakest perturbation capable to disrupt the system and switch it to an undesired dynamical regime. In the phase space, the stability threshold corresponds to the "thinnest site" of the attraction basin and therefore indicates the most "dangerous" direction of perturbations. We introduce a computational algorithm for quantification of the stability threshold and demonstrate that the suggested approach is effective and provides important insights. The generality of the obtained results defines their vast potential for application in such fields as engineering, neuroscience, power grids, Earth science and many others where robustness of complex systems is studied.
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