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

TL;DR

This paper investigates how slow chaotic driving induces multistability and various forms of remote synchronization in Chua's circuit, revealing new synchronization phenomena and attractor behaviors.

Contribution

It demonstrates that slow chaotic drive causes multistability and novel remote synchronization states in Chua's circuit, expanding understanding of driven chaotic systems.

Findings

Multistability occurs at low drive frequencies and high driving strength.

Different forms of remote synchronization, including lag synchronization, are observed.

Multistability disappears as drive frequency increases, restoring single attractor behavior.

Abstract

We study the response of Chua's circuit driven by a chaotic signal of variable time-scale. We observe that when the frequency of the drive is significantly lower than that of the response and the driving strength is above a threshold, the Chua's circuit exhibits multiple stable attractors. The features of the attractors change as the driving strength {\epsilon} increases, for instance the attractors are double-scroll at low {\epsilon} and are single-scroll when {\epsilon} 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 drive increases and become equivalent to the response Chua's ciruit.