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A relatively simple chaotic hyperjerk circuit, which is the modified chaotic hyperjerk system [Dalkiran and Sprott, IJBC 2016] is proposed and investigated in this paper. Only one semiconductor diode modelled the nonlinear function capable of rich and complex dynamical behaviours of the system. We investigate a new kind of behaviours name “bubbles of bifurcation’’ (referred as BsB hereafter) observed here for the first time in the hyperjerk system. An interesting phenomenon of mixed-mode bursting oscillations (MMBOs) is also investigated. The complex dynamics of the novel oscillator (such as MMBOs, BsB, offset boosting and multistability) with respect to its parameters and initial conditions are uncovered using bifurcation diagrams, Lyapunov exponents (LE) and phase portraits. As another interesting property of this circuit, some parameter regions are determined for the existence of coexisting BsB and the coexistence of asymmetric mixed-mode bursting oscillations. Let us emphasized that the complex phenomena observed in this work is very rare in the literature and henceforth merit dissemination. Finally, a physical circuit is constructed to demonstrate some experimental observation of MMBOs.

A modified simple chaotic hyperjerk circuit: coexisting bubbles of bifurcation and mixed-mode bursting oscillations