Dynamics and bifurcations of fuzzy nonlinear dynamical systems
type: Item
instance of: scholarly article
title: Dynamics and bifurcations of fuzzy nonlinear dynamical systems
zbMATH Open document ID: 1386.34005
published in: Fuzzy Sets and Systems
publication date: 2018-02-20T00:00:00Z
review text: This paper investigates the bifurcation of fuzzy solutions to nonlinear fuzzy dynamical systems obtained by applying the extension principle of Zadeh. The authors define the concept of fuzzy bifurcation value following the standard approach used in the analysis of dynamical systems for more general metric spaces and further define concepts from bifurcation theory such as topological equivalence of fuzzy flows and fuzzy bifurcation values. Furthermore, they study the effects of parameters on the asymptotic behaviors of fuzzy solutions and show that fuzzy solutions inherit bifurcation values from deterministic solutions and generalize some previous results. The main result shows that if a deterministic bifurcation value belongs to a fuzzy parameter, then this fuzzy parameter is a fuzzy bifurcation value for the fuzzy solution. The authors illustrate the results obtained from this study with some example of one-dimensional nonlinear dynamical systems.
reviewed by: Andrej V. Plotnikov
Mathematics Subject Classification ID: 34A07
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 34D05
Mathematics Subject Classification ID: 34C41
zbMATH DE Number: 6841031
zbMATH Keywords: bifurcation values
zbMATH Keywords: Zadeh extension principle
zbMATH Keywords: asymptotic behavior
zbMATH Keywords: topological equivalence
author: Marina T. Mizukoshi
author: Moiseis S. Cecconello
MaRDI profile type: Publication
full work available at URL: j.fss.2016.11.012
OpenAlex ID: W2557401404
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DOI: 10.1016/J.FSS.2016.11.012
description: scientific article; zbMATH DE number 6841031