Remerging Feigenbaum trees, and multiple coexisting bifurcations in a novel hybrid diode-based hyperjerk circuit with offset boosting

Abstract

This paper proposes a novel chaotic hyperjerk circuit obtained from the autonomous 4-D hyperjerk circuit (Leutcho et al. in Chaos Solitons Fractals 107:67–87, 2018) via substituting the nonlinear component (pair of anti-parallel diodes) with a first order hybrid diode circuit. The nonlinear component (i.e. hybrid diode) is characterized by a frequency dependent nonlinear I–V characteristic which is responsible for complex behaviours of the whole circuit. The essential dynamic properties of the model are investigated by exploiting numerical tools of nonlinear theory such as bifurcation diagrams, graphs of Lyapunov exponents, as well as phase portraits. Some interesting features are found including period-doubling bifurcation, coexisting bifurcations, symmetry recovering crises, antimonotonicity, and offset-boosting. One of the most interesting features of the new hyperjerk circuit is the presence of various areas of parameter space in which the hyperjerk system exhibits the attractive and intricate property of coexisting bifurcation and several coexisting attractors (e.g. coexistence of two, three, four, five, six, or seven disconnected periodic and chaotic attractors) for the same parameter’ set. Laboratory experimental results show a very good agreement with the theoretical analysis.