A novel chaotic hyperjerk circuit with bubbles of bifurcation: mixed-mode bursting oscillations, multistability, and circuit realization

Abstract

This contribution proposes a novel chaotic hyperjerk circuit with the new phenomenon of mixed-mode bursting oscillations (MMBOs). The bifurcation analysis of this specific oscillator reveals a relatively rare and complex phenomenon of various coexisting two full Feigenbaum remerging trees. Common nonlinear dynamic systems analysis tools such as bifurcation diagram, phase portraits, time series and Lyapunov exponent are used to uncover the complex behaviours of the circuit with respect to its parameters and initial conditions as well. As one of the major contributions of this work, we introduce a novel hyperjerk circuit with rare phenomena such as the coexistence of a new phenomenon named bubbles of bifurcation (referred as BsB hereafter), the coexistence of two or three asymmetric mixed-mode bursting oscillations, just to name a few. All these phenomena are found simultaneously in a single circuit and thus diverse dissemination. Experimental results support the theoretical analysis.