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. To make the circuit low power consumption and portable in practice, it is fully integrated. In the paper, a periodic excitation and different piecewise functions are introduced into the system which leads to two types of piecewise-smooth 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. 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.