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

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...

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Autores principales: Chen, Lianyu, Nazarimehr, Fahimeh, Jafari, Sajad, Tlelo-Cuautle, Esteban, Hussain, Iqtadar
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2020
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7516801/
https://www.ncbi.nlm.nih.gov/pubmed/33286115
http://dx.doi.org/10.3390/e22030341
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author Chen, Lianyu
Nazarimehr, Fahimeh
Jafari, Sajad
Tlelo-Cuautle, Esteban
Hussain, Iqtadar
author_facet Chen, Lianyu
Nazarimehr, Fahimeh
Jafari, Sajad
Tlelo-Cuautle, Esteban
Hussain, Iqtadar
author_sort Chen, Lianyu
collection PubMed
description 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.
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spelling pubmed-75168012020-11-09 Investigation of Early Warning Indexes in a Three-Dimensional Chaotic System with Zero Eigenvalues Chen, Lianyu Nazarimehr, Fahimeh Jafari, Sajad Tlelo-Cuautle, Esteban Hussain, Iqtadar Entropy (Basel) Article 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. MDPI 2020-03-17 /pmc/articles/PMC7516801/ /pubmed/33286115 http://dx.doi.org/10.3390/e22030341 Text en © 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Chen, Lianyu
Nazarimehr, Fahimeh
Jafari, Sajad
Tlelo-Cuautle, Esteban
Hussain, Iqtadar
Investigation of Early Warning Indexes in a Three-Dimensional Chaotic System with Zero Eigenvalues
title Investigation of Early Warning Indexes in a Three-Dimensional Chaotic System with Zero Eigenvalues
title_full Investigation of Early Warning Indexes in a Three-Dimensional Chaotic System with Zero Eigenvalues
title_fullStr Investigation of Early Warning Indexes in a Three-Dimensional Chaotic System with Zero Eigenvalues
title_full_unstemmed Investigation of Early Warning Indexes in a Three-Dimensional Chaotic System with Zero Eigenvalues
title_short Investigation of Early Warning Indexes in a Three-Dimensional Chaotic System with Zero Eigenvalues
title_sort investigation of early warning indexes in a three-dimensional chaotic system with zero eigenvalues
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7516801/
https://www.ncbi.nlm.nih.gov/pubmed/33286115
http://dx.doi.org/10.3390/e22030341
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