Synchronization and Waves in a Ring of Diffusively Coupled Memristor-Based Chua's Circuits

In the present paper we report numerical observations of the spontaneous dynamics of N identical memristor-based Chua's circuits bidirectionally coupled in a ring geometry. Two different initial configurations are studied by varying N and the coupling strength: in the first configuration we consider only one circuit with non-zero initial conditions, in the second one all circuits have uniform random initial conditions. We observed both chaotic and non-chaotic synchronization. In the chaotic synchronized regime we identified emerging chaotic steady waves, characterized by an almost constant frequency and chaotic amplitude. Depending on the initial conditions, in the pseudo-sinusoidal oscillations regime both macroscopic quasi-periodic steady and traveling waves were observed.