Hyperchaotic Synchronization

In this work we study the synchronization between identical pairs of hyperchaotic mathematical systems symmetrically coupled. Calculations are performed firstly in two well-known hyperchaotic systems, and then compared with the results obtained coupling symmetrically two Takens–Bogdanov systems (TBS) which represent a bifurcation in Codimension 2 (a point with two modes bifurcating simultaneously). In all of these systems, complete synchronization is achieved for some intervals of the coupling strength. As it will be shown, these windows can be localized by using the representation of the Lyapounov exponents against the coupling parameter. We analyze here these three models looking for general features in synchronization of hypercaotic systems, that could be useful to model mutual synchronization of two timedependent convection experiments. We plan to use the results obtained in the TBS as a direct guide to control our experiment because this model was successfully used before to represent the observed dynamics. The other two systems presented here (Chen and Lü) are used to look for the possibility of general features and to check the used numerical methods.