Sándor Bulcsú, Schneider Bence, Lázár Zsolt I, Ercsey-Ravasz Mária
Department of Physics, Babes-Bolyai University, 400084 Cluj-Napoca, Romania.
Network Science Lab, Transylvanian Institute of Neuroscience, 400157 Cluj-Napoca, Romania.
Entropy (Basel). 2021 Jan 12;23(1):103. doi: 10.3390/e23010103.
The combination of network sciences, nonlinear dynamics and time series analysis provides novel insights and analogies between the different approaches to complex systems. By combining the considerations behind the Lyapunov exponent of dynamical systems and the average entropy of transition probabilities for Markov chains, we introduce a network measure for characterizing the dynamics on state-transition networks with special focus on differentiating between chaotic and cyclic modes. One important property of this Lyapunov measure consists of its non-monotonous dependence on the cylicity of the dynamics. Motivated by providing proper use cases for studying the new measure, we also lay out a method for mapping time series to state transition networks by phase space coarse graining. Using both discrete time and continuous time dynamical systems the Lyapunov measure extracted from the corresponding state-transition networks exhibits similar behavior to that of the Lyapunov exponent. In addition, it demonstrates a strong sensitivity to boundary crisis suggesting applicability in predicting the collapse of chaos.
网络科学、非线性动力学和时间序列分析的结合为研究复杂系统的不同方法提供了新的见解和类比。通过结合动力系统李雅普诺夫指数背后的考量因素以及马尔可夫链转移概率的平均熵，我们引入了一种网络度量，用于刻画状态转移网络上的动力学，特别关注区分混沌模式和循环模式。这种李雅普诺夫度量的一个重要特性是它对动力学循环性的非单调依赖性。为了为研究这种新度量提供合适的应用案例，我们还提出了一种通过相空间粗粒化将时间序列映射到状态转移网络的方法。使用离散时间和连续时间动力系统，从相应状态转移网络中提取的李雅普诺夫度量表现出与李雅普诺夫指数相似的行为。此外，它对边界危机表现出强烈的敏感性，表明其在预测混沌崩溃方面具有适用性。
