Dual Memristive Chua’s Circuit

As a paradigm bridging the mathematical chaos to physical one, Chua’s circuit and its dimensionless Chua’s system have been widely studied and applied. From the completeness point of view, it is an interesting issue under investigation that how many potential Chua’s circuit variants exist within the framework of a single Chua’s system. Follow the duality principle in electrical circuits, this paper presents a Chua’s circuit employing ideal charge-controlled memristive model, which complements the circuit genealogy of the classical Chua’s system to four, i.e., Chua’s circuit, dual Chua’s circuit, memristive Chua’s circuit, and dual memristive Chua’s circuit (DMCC). To study the initial condition-related dynamical behaviors of the DMCC, we further present the flux-charge analysis. Some complex coexisting dynamics that cannot be typically observed in the voltage-current-domain have been investigated in the flux-charge-domain. Based on the dimensionless equations of the DMCC, an equivalent circuit is implemented for verification.