Complexity and emergence of wave dynamics in a chain of sequentially interconnected Chua circuits

This paper considers an ensemble of Chua oscillators bidirectionally coupled in a ring geometry where locally coupled circuits form a closed loop of signal transmission. The spontaneous dynamics of this system is studied numerically for different coupling strength. A transition from periodic to chaotic regimes is observed when the coupling decreases. In the former situation, characterized by high coupling, all the circuits oscillate with pseudo-sinusoidal dynamics on periodic attractors; in the latter they evolve on the same-type of chaotic attractor with a progression of the dynamics from the Chua's spiral to the double scroll as the coupling decreases. The emerging global dynamics is markedly different in the two cases and a phase transition between highly ordered and highly disordered global dynamics is observed. Synchronization and traveling waves moving along the ring are identified in the non-chaotic regime, while spatio-temporal chaos results for very low coupling. Complex patterns formation appears at the “edge of chaos”, for a small couplings interval after the transition between these two regimes.