Coupling induced topological transition in a ring of chaotic oscillators

A ring of diffusively coupled R?ssler oscillators, which can develop the conventional rotating wave from high-dimensional chaos by increasing the coupling ɛ continuously is studied. The chaotic generator for the rotating wave emerges around ɛ = ɛ, where the topological transition induced by the coupling not only changes the topological structure of all the oscillators, which share a common strange attractor, but also changes them into being different from each other. Starting from this transition, infinitely long range temporal correlation and spatial order in the style of antiphase state are established gradually, which gives rise to the chaotic generator of the rotating wave. Received 15 March 2001