On the topological equivalence of some fuzzy flows near hyperbolic equilibria

Authors:
Marina T. Mizukoshi;LaéCio C. Barros;Rodney C. Bassanezi;Adilson J. V. BrandãO
Affiliations:
Institute of Mathematics and Statistics, Federal University of Goiás, Goiânia, Brazil;Department of Applied Mathematics, IMECC, University of Campinas, Campinas, Brazil;Center of Mathematics, Computation and Cognition, CMCC, Federal University of ABC, Santo André, Brazil;Federal University of São Carlos, Campus Sorocaba, Sorocaba, Brazil
Venue:
Fuzzy Sets and Systems
Year:
2012

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Abstract

The purpose of this work is to study fuzzy dynamical systems associated with deterministic systems. The Grobman-Hartman theorem states that, near hyperbolic equilibria, there exists a homeomorphism between the nonlinear system's trajectories and the linearized correspondent system's trajectories. That is, these systems are topologically equivalent. A theorem similar to Grobman-Hartman theorem to fuzzy flows is the main result in this article. For fuzzy flows obtained from each system it states that the nonlinear and the linearized are topologically equivalent.