Symbolic Dynamics and Chaotic Synchronization in Coupled Duffing Oscillators

Abstract

In this work we discuss the complete synchronization of two identical double-well Duffing oscillators unidirectionally coupled, from the point of view of symbolic dynamics. Working with Poincaré cross-sections and the return maps associated, the synchronization of the two oscillators, in terms of the coupling strength, is characterized. We obtained analytically the threshold value of the coupling parameter for the synchronization of two unimodal and two bimodal piecewise linear maps, which by semi-conjugacy, under certain conditions, gives us information about the synchronization of the Duffing oscillators.

Topological Entropy in the Synchronization of Piecewise Linear and Monotone Maps: Coupled Duffing Oscillators

“…In a previous work [Caneco et al, 2008] we try to understand the relationship between the achievement of synchronization and the evolution of the symbolic sequences S x and S y , obtained for the x and y coordinates, as described in subsection 3.2.. We verify that, as the value of the coupling parameter k increases, the number of initial equal symbols in the S x and S y sequences increases also, which is a numerical symbolic evidence that the two systems are synchronized.…”

Symbolic dynamics and chaotic synchronization

“…In a previous work we have found in the parameter plane ) , (   regions U and B where the first return Poincaré map behaves like a unimodal map and like a bimodal map respectively, see [4]. We computed the kneading sequences, the kneading determinant and the topological entropy for some values of the parameters ) , (   , see [2] and [4]. The synchronization will occur when y x  .…”