Spatiotemporal Pattern Formation in a Ring of Chua’s Oscillators

In the present work the spontaneous dynamics of a ring of $N$ Chua's oscillators, mutually coupled through a resistor $R_c$ in a nearest-neighbor configuration, is investigated numerically for different strengths of the coupling. A transition from periodic to chaotic global dynamics is observed when the coupling decreases below a critical value and complex patterns in the spatiotemporal dynamics of the ring emerge for a small coupling interval after the transition to chaos. The recovered behavior, as well as the value of the critical threshold, appears to be independent of the size of the ring. We also propose an interpretation of this property, which relates the regular synchronized dynamics of the ring to the dynamics of the isolated oscillator. Finally, for the ring of the coupled oscillator, a theoretical wave dispersion relation is calculated and successfully compared with the results of the numerical simulations, analyzed by classical techniques adopted for turbulent flows.