具有零特征值的三维混沌系统中的早期预警指标研究

Investigation of Early Warning Indexes in a Three-Dimensional Chaotic System with Zero Eigenvalues.

作者信息

Chen Lianyu, Nazarimehr Fahimeh, Jafari Sajad, Tlelo-Cuautle Esteban, Hussain Iqtadar

机构信息

School of Electrical and Information Engineering, Jiangsu University of Technology, Changzhou 213001, China.

Department of Biomedical Engineering, Amirkabir University of Technology, 424 Hafez Ave., Tehran 15875-4413, Iran.

出版信息

Entropy (Basel). 2020 Mar 17;22(3):341. doi: 10.3390/e22030341.

DOI:10.3390/e22030341

PMID:33286115

原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC7516801/

Abstract

A rare three-dimensional chaotic system with all eigenvalues equal to zero is proposed, and its dynamical properties are investigated. The chaotic system has one equilibrium point at the origin. Numerical analysis shows that the equilibrium point is unstable. Bifurcation analysis of the system shows various dynamics in a period-doubling route to chaos. We highlight that from the evaluation of the entropy, bifurcation points can be predicted by identifying early warning signals. In this manner, bifurcation points of the system are analyzed using Shannon and Kolmogorov-Sinai entropy. The results are compared with Lyapunov exponents.

摘要

提出了一种所有特征值都等于零的罕见三维混沌系统，并对其动力学特性进行了研究。该混沌系统在原点处有一个平衡点。数值分析表明该平衡点是不稳定的。对该系统的分岔分析显示了在倍周期通向混沌的路径中存在各种动力学行为。我们强调，通过评估熵，可以通过识别早期预警信号来预测分岔点。通过这种方式，使用香农熵和柯尔莫哥洛夫-西奈熵对系统的分岔点进行了分析。将结果与李雅普诺夫指数进行了比较。