Hybrid-Diode-Based Shinriki Circuit: Coexisting Oscillations and Bifurcation Trees

Abstract

Nonlinear circuit can exhibit complex dynamical behaviors, especially the coexisting periodic or chaotic oscillations, by employing various electronic elements. However, oscillation circuits with a simple hybrid diode, which can induce richer dynamical behaviors with only a pair of anti-parallel diodes and an RC filter, are rarely reported, thus hindering the deep cognition and potential applications of such nonlinear circuits. This paper focuses on the dynamical behaviors of a Shinriki circuit modified by applying the hybrid diode, in which multiple coexisting oscillations and antimonotonic evolutions are successfully discovered by varying circuit parameters. To deeply study these phenomena, a discrete mapping structure of the proposed circuit is constructed by the semi-analytical method, and the bifurcation trees of diverse coexisting periodic oscillations are thoroughly investigated via bifurcation diagrams and phase portraits. The emergence and disappearance of antimonotonic phenomena with stable and unstable orbits are also clearly revealed. Notably, the stability and bifurcation points of the motions are precisely judged by eigenvalues, and the unstable routes hidden in chaotic regions can be uncovered. Finally, the coexisting stable and unstable periodic orbits are captured from the oscilloscope via a field programmable gate array (FPGA), which verifies the correctness of the analysis. The research may be devoted to the improvement of nonlinear circuit.