DC-offset-induced hidden and asymmetric dynamics in Memristive Chua's circuit

Mo Chen, Ankai Wang, Chao Wang, Huagan Wu and Bocheng Bao

Chaos, Solitons & Fractals, 2022, vol. 160, issue C

Abstract: Hidden attractors have been discovered in classical Chua's circuits with special Chua's diode nonlinearities. But designing such physical Chua's circuits is a challenge due to the distinct slopes of Chua's diodes. The analog-circuit-based measurements of hidden dynamical behaviors are also difficult since their attraction basins are relatively small and independent of any equilibrium points. In this paper, a DC-offset method is proposed for obtaining hidden dynamics from preexisting nonlinear circuits. An improved memristive Chua's circuit with hidden dynamical behaviors is constructed by inserting a DC voltage source into the inductor branch therein. The DC-offset-induced hidden and asymmetric dynamical behaviors are revealed via equilibrium point analyses, numerical simulations, and experimental measurements. The coexistence of hidden attractors is demonstrated when the modified memristive Chua's circuit possesses at least one unstable equilibrium point or only one stable equilibrium point. Furthermore, a reconstituted model is formulated using the incremental integral transformation method to facilitate the measurements of hidden and coexisting attractors having relatively small attraction basins. With this model, the self-excited and hidden properties of the coexisting attractors are maintained, while their attraction basins are transferred to the neighborhood of the easily circuit-implemented origin point. Thus, the existence of hidden and coexisting attractors is readily verified via hardware circuit measurements.

Keywords: Memristive Chua's circuit; DC-offset; Equilibrium point; Hidden attractor; Asymmetric attractor; Multistability (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (7)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:160:y:2022:i:c:s0960077922004027

DOI: 10.1016/j.chaos.2022.112192

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