Complex Dynamics of a Linear Coupling of Two Chaotic Lorenz Systems

In this manuscript, we report on aspects of dynamical behaviors of a continuous-time autonomous six-dimensional system, wich was designed by bidirectionally coupling two chaotic Lorenz systems through a linear function. The two-dimensional parameter-space generated by considering the parameters a and c present in the coupling function is investigated. We show that the considered bidirectional coupling is responsible for the occurrence of chaos suppression, characterized by the presence of periodic and quasiperiodic regions in the (a, c) parameter-space of the coupled system. As a consequence of the coupling, hyperchaos regions with two positive Lyapunov exponents also are observed in the (a, c) parameter-space. We also show that the (a, c) parameter-space exhibits periodic structures embedded in chaotic regions, being their periods organized in period-adding sequences, whose period increment rate is equal to the period of the region on whose boundary the structures accumulate.