Bursting oscillations and bifurcation mechanism in a fully integrated piecewise-smooth chaotic system

Abstract

This paper aims to show and investigate bursting oscillator and bifurcation phenomena in a piecewise-smooth memristor-based Shimizu–Morioka (SM) system. First, a piecewise-smooth nonlinear system is built. Second, considering the memory characteristic of the memristor and the formation of the bursting oscillations circuit, a memristor and a periodic excitation are introduced into the system which leads to the piecewise-smooth memristor-based systems with a single slow variable. As the slow variable changes periodically in different scopes, we discover intricate bursting oscillation phenomena, namely, asymmetric Fold/Fold bursting, damped oscillation-sliding, asymmetric Fold/Fold-delayed supHopf/supHopf bursting, compressed oscillation phenomenon within the limit cycle, random bursting, double loop oscillations and so on. To make the circuit low power consumption and portable in practice, it is fully integrated. In the course of the study, it is found that the properties of the nominal equilibrium orbits, limit cycles, and the non-smooth boundary contribute to the bursting. Finally, a fully integrated circuit is designed and the accuracy of the study is verified by some circuit simulation results.