On the topological equivalence of some fuzzy flows near hyperbolic equilibria

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 systemʹs trajectories and the linearized correspondent systemʹs 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.