Complete Synchronization between Hiperchaotic Space-Time Attractors

Abstract

Many dynamical processes that occur in nature or in experiments are space-time bifurcations in systems with symmetries. One of the most outstanding examples of such bifurcations is the Takens-Bogdanov bi- furcation [1] that has been used to model Codimension-two bifurcations with double zero eigenvalues and square symmetries, that exhibit chaotic behavior [2, 3]. In particular, the dynamics of termo-convective experi- ments in square cells with a small aspect ratio have been modeled with the groups of symmetry Z2 [4] and D4 [5]. In the first part of this work we describe the dynamic behavior appear- ing in the equation system with the group of symmetry D4 proposed in [2], as a function of the different parameters. The space of parameters is analyzed in order to identify those variables that could be useful to synchronize, in space and time, two identical systems of this kind. In the second part we describe the first results obtained to synchronize two identical systems.