Dynamics and transitions of the coupled Lorenz system

In this paper, we are interested in a very simple and fundamental question: Is the dynamics of a coupled chaotic system always chaotic? It is found that in addition to the expected complicated chaos and hyperchaos, two identical Lorenz systems starting at different initial conditions and coupling together via nonfeedback-type interactions can also exhibit simple dynamics such as fixed points, limit cycles, and tori in wide parametric ranges of coupling constants. Also, in the parametric space of coupling constants, four distinct routes of dynamical transitions are found for this simple coupled system. Along the route of dynamical transitions, intermittence, sideband instability, and nonlinear interactions of dynamical modes are all involved.