Design and Implementation of Grid-Wing Hidden Chaotic Attractors With Only Stable Equilibria

Due to complex chaotic characteristics and multistable states, the generation of multi-wing hidden chaotic attractors shows a new application prospect in chaos-based security communication. However, for chaotic systems with multiple stable equilibria, the point attractors have attraction basins that are separately embedded in the initial value space, which makes it difficult to generating bands to connect different wings or scrolls. Up to now, grid-wing hidden chaotic attractors with only stable equilibria have not been reported yet. In this paper, a novel system for generating symmetric and asymmetric hidden chaotic attractors is proposed. By applying symmetric piecewise-linear modulation functions to a seed system with only two stable equilibria, multiple stable equilibria with single-direction pair distribution and two-direction grid distribution are configured. Principle of the key technique is based on the offset switch, which effectively connect different wings via the switch bands. Consequently, multi-wing, multi-double-wing, and grid-wing hidden chaotic attractors are generated. Besides, applying asymmetric modulation functions lead to the generation of asymmetric multi-wing hidden chaotic attractor. Attraction basins of various multi-wing and grid-wing hidden attractors are investigated to show the multistability. Numerical simulations and corresponding FPGA-based physical experiments validated the feasibility of the generation method.