Dynamics and bifurcations of fuzzy nonlinear dynamical systems
Copyright policy )Dynamics and bifurcations of fuzzy nonlinear dynamical systems
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.
Bifurcation theory for ordinary differential equations, bifurcation values, Fuzzy ordinary differential equations, Zadeh extension principle, Equivalence and asymptotic equivalence of ordinary differential equations, asymptotic behavior, Asymptotic properties of solutions to ordinary differential equations, topological equivalence
Bifurcation theory for ordinary differential equations, bifurcation values, Fuzzy ordinary differential equations, Zadeh extension principle, Equivalence and asymptotic equivalence of ordinary differential equations, asymptotic behavior, Asymptotic properties of solutions to ordinary differential equations, topological equivalence
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