Slow-driving-induced multistability and remote synchronization in chaotic Chua's circuit

We study the response of Chua's circuit driven by a chaotic signal of variable timescale. We observe that when the frequency of the driving signal is significantly lower than that of the response and the driving strength is above a threshold, Chua's circuit exhibits multiple stable attractors. The features of the attractors change as the driving strength ɛ increases; for instance, the attractors are double-scroll at low ɛ and are single-scroll when ɛ is high. We also investigate generalized synchronization (GS) between the drive and the response systems by employing the auxiliary system approach. When the drive is much slower than the response, we observe different scenarios of remote synchronization (RS) between response and auxiliary units. In addition to complete synchrony between response and auxiliary systems indicating GS between drive and response, we notice that the response and auxiliary units can be lag-synchronized and can also have correlated trajectories indicating novel forms of RS. The slow drive can induce multistability between these RS states, which disappears as the frequency of the driving signal increases and becomes equivalent to that of the response of Chua's circuit.