Dynamical analysis of a novel autonomous 4-D hyperjerk circuit with hyperbolic sine nonlinearity: Chaos, antimonotonicity and a plethora of coexisting attractors

In this paper, a novel fourth-order autonomous hyperjerk circuit is proposed and the corresponding dynamics is systematically analyzed. Two anti-parallel semiconductor diodes form the nonlinear component necessary for chaotic oscillations. The mathematical model of the novel circuit consists of a fourth-order (“elegant”) autonomous hyperjerk system with (a single) hyperbolic sine nonlinearity. The fundamental dynamic properties of the model are investigated including fixed points and stability, phase portraits, bifurcation diagrams, and Lyapunov exponent plots. Period-doubling bifurcation, periodic windows, coexisting bifurcations, symmetry recovering crises, and antimonotonicity (i.e. concurrent creation and annihilation of periodic orbit) are reported when monitoring the systems parameters. One of the main findings in this work is the presence of various windows in the parameter space in which the novel 4D-hyperjerk system develops the interesting property of multiple coexisting attractors (e.g. coexistence of two, three, four, five, six, seven height or nine disconnected periodic and chaotic attractors). To the best of the authors’ knowledge, this striking phenomenon is unique and has not yet been reported previously in a hyperjerk circuit, and thus represents a significant contribution to the understanding of the behavior of nonlinear dynamical systems in general. Laboratory experiments of the oscillator are carried out to verify the theoretical analysis.