Coexisting Multiple Attractors in a Fourth Order Chua’s Circuit With Experimental Verifications by Analog and Digital Circuits

Abstract

Exploring coexistence of multiple attractors brought by the multistability for circuits and systems has a significant meaning in the theoretical researches and practical applications for chaos. In this article, a succinct fourth order Chua’s circuit is proposed by replacing the negative resistance with an ordinary positive resistance in a traditional fourth order one. The two-dimensional stability analysis for equilibrium points shows that this circuit possesses one unstable saddle-focus point with index 1 and two stable node-focus points. Coexisting bifurcation models, multiple attractors and the corresponding attraction basins are revealed by a series of numerical simulations. The clear crisis scenario of the coexisting limit cycles of period-3 bridging the coexisting single-scroll attractors of chaos and the double-scroll one is observed by the bifurcation analyses. The dual-mode experimental verifications by the analog and digital circuits are carried out on the self-made printed circuit boards, which validate the simulated dynamical behaviors with the combination of physics and engineering.