Grid Hyperchaotic System With Stable Equilibria

Abstract

The generation of complicated grid hyperchaotic hidden attractors is an interesting but challenging work. Up to now, no grid hyperchaotic system with stable equilibria has been reported and implemented yet. This paper presents a two-step design scheme for constructing novel grid hyperchaotic system with only stable equilibria. First, the simple variable boosting is applied to a single-stable-equilibrium hyperchaotic system to generate offset boosted hyperchaotic hidden attractors in two directions. At this point, it is associated with the increase of the number of equilibria in corresponding directions. To solve this problem, the configuration of two specific sawtooth waveform functions implements the offset switching in two directions but only extends the number of the equilibria in a single direction. Meanwhile, all these equilibria have the same stability conditions that will not change with the increase of the grid. Consequently, various grid hyperchaotic hidden attractors are generated. Numerical simulations are presented to intuitively show the phase portraits and cross sections. Finally, hardware experiments using analog circuit implementation are presented to verify the feasibility of the grid hyperchaotic system.