A unique self-driven 5D hyperjerk circuit with hyperbolic sine function: Hyperchaos with three positive exponents, complex transient behavior and coexisting attractors

We propose a new hyperchaotic hyperjerk-type electronic circuit of remarkable simplicity composed only of simple electronic components. The mathematical model of the circuit, derived by application of Kirchhoff's laws, is presented in the form of a hyperjerk system of order five with a single nonlinearity in the form of hyperbolic sine. The model owns a single unstable equilibrium at the origin. The theoretical analysis yields striking dynamical features including the hyperchaos with three positive Lyapunov exponents, complex transient, coexisting multiple attractors and offset boosting. These properties are illustrated using eigenvalues locus, the plot of bifurcation diagrams, time series, basins of attraction, phase portraits, Poincaré sections as well as the spectrum of Lyapunov exponents. The measurements carried out in the laboratory on an experimental prototype are consistent with the results of the theoretical study. Let us mention that the presence of three positive Lyapunov exponents for an autonomous system of order five with such a simple mathematical model is unprecedented in the literature and deserves to be shared.