On the First Hyperchaotic Hyperjerk System With No Equilibria: A Simple Circuit for Hidden Attractors

A fourth-order hyperchaotic hyperjerk system with no equilibria has never been reported, whereas a search for its existence has been an open research problem. A new system in a rare type of 4D seven-term no-equilibrium hyperchaotic systems is proposed and also compared with two existing systems of such a rare type. The proposed system offers 10 concurrent advantages, six of which appear to be superior to both existing systems, that is; 1) the first report of a fourth-order hyperchaotic hyperjerk system with no equilibria; 2) a much simpler circuit based on only 21 electronic components; 3) a higher value of the Lyapunov dimension at 3.2280; 4) a higher value of the largest Lyapunov exponent at 0.2525; 5) a large two-parameter space of hyperchaos; and 6) a boostable variable for offset control. The other four advantages offer either equal or better features, that is; 7) the number of nonlinear terms is two; 8) no potential dangers of multistability; 9) hyperchaos, chaos, and periodic behavior are possible; and 10) attractors are readily hidden attractors. The system is unique in the sense that there are no equilibria in both dynamical and hyperjerk forms.

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