Basin stability in delayed dynamics.
Basin stability in delayed dynamics.
复制标题
延迟动力学中的盆地稳定性
DOI：
10.1038/srep21449
复制
发表时间：
2016-02-24
影响因子：
4.6
通讯作者：
Kurths J
中科院分区：
文献类型：
--
作者：
Leng S;Lin W;Kurths J
流域稳定性是复杂系统研究中的一个普遍概念，它侧重于吸引流域的体积，而不是传统的基于线性化的方法。它在现实世界的系统中有很多应用，特别是在具有多稳定性现象的动力系统中，这在延迟动力学中更加普遍，如放电神经元，气候过程和电网。由于初始值空间的无穷维性质，如何正确地定义盆地的延迟动力学的体积仍然是一个基本问题。本文提出了一种将无限维初始状态空间投影到有限维欧氏空间的方法，即通过将初始函数沿着以不同的正交或非正交基展开。本文提出了时滞动力学中吸引域体积的广义概念，并给出了一种实用性强的计算算法和交叉验证程序，用于时滞动力学中吸引域的数值估计。我们显示了这种方法的潜在适用性，通过应用它来研究几个代表性的系统的生物或/和物理意义，包括延迟Hopfield神经元模型与多稳定性和延迟复杂网络的同步动力学。
Basin stability (BS) is a universal concept for complex systems studies, which focuses on the volume of the basin of attraction instead of the traditional linearization-based approach. It has a lot of applications in real-world systems especially in dynamical systems with a phenomenon of multi-stability, which is even more ubiquitous in delayed dynamics such as the firing neurons, the climatological processes and the power grids. Due to the infinite dimensional property of the space for the initial values, how to properly define the basin’s volume for delayed dynamics remains a fundamental problem. We propose here a technique which projects the infinite dimensional initial state space to a finite-dimensional Euclidean space by expanding the initial function along with different orthogonal or nonorthogonal basis. A generalized concept of basin’s volume in delayed dynamics and a highly practicable calculating algorithm with a cross-validation procedure are provided to numerically estimate the basin of attraction in delayed dynamics. We show potential applicabilities of this approach by applying it to study several representative systems of biological or/and physical significance, including the delayed Hopfield neuronal model with multistability and delayed complex networks with synchronization dynamics.