Complexity control in a synchronized complex system

Abstract

We numerically analyze the problem of how to drive a synchronized state in a complex system to other state with diferent complexity, keeping synchronization. The complex system used is obtained by synchronizing two identical chaotic Takens-Bogdanov sub-systems specially coupled to recover in the global system the symmetries of each oscillator. The global state is adjusted to have an initial synchronized hyperchaotic state (with two positive Lyapunov exponents). This work is an attempt, using small amplitude external signals, to drive the global system to other complex state keeping the synchronized state. The method used to overcome the problems that we had to select a useful frequency value for the driving signal will be discussed, together with a possible experiment in a thermo-convective flow for validating the results obtained.