Symbolic Dynamics Generated by a Hybrid Chaotic Systems
Carlos Correia Ramos
Department of Mathematics, CIMA, University of Évora, Rua Romão Ramalho 59, 7000-671 Évora, Portugal
Ana Isabel Santos *
Department of Mathematics, CIMA, University of Évora, Rua Romão Ramalho 59, 7000-671 Évora, Portugal
Sandra Vinagre
Department of Mathematics, CIMA, University of Évora, Rua Romão Ramalho 59, 7000-671 Évora, Portugal
*Author to whom correspondence should be addressed.
Abstract
We consider piecewise defined differential dynamical systems which can be analysed through symbolic dynamics and transition matrices. We have a continuous regime, where the time flow is characterized by an ordinary differential equation (ODE) which has explicit solutions, and the singular regime, where the time flow is characterized by an appropriate transformation. The symbolic codification is given through the association of a symbol for each distinct regular system and singular system. The transition matrices are then determined as linear approximations to the symbolic dynamics. We analyse the dependence on initial conditions, parameter variation and the occurrence of global strange attractors.
Keywords: Dynamical systems, symbolic dynamics, iteration theory, transition matrices, attractors