Dynamic behaviour of two coupled Lorenz systems

In this paper, the dynamics of a nonlinear bidirectional coupling of two Lorenz systems is analyzed. The coupling is realized trough polynomial functions composed by quadratic terms of the system state variables. The analysis of the transverse and tangent systems ensures the absence of synchronization between the subsystems. It is demonstrated that with this choice of the coupling functions, the system dynamics is not hyperchaotic in spite of the presence of two positive Lyapunov exponents.