Here, a 4-D hyper-chaotic system with only one equilibrium point was constructed to reveal rich multi-stable characteristics with multi-wing attractors. The system’s dynamic characteristics were numerically analyzed, and the system’s analog circuit and digital circuit were simulated to explore the dynamic complexity of the system, and test the randomness of the system’s hyper-chaotic sequences. The analysis results showed that under multi-set of system parameters, there are coexistences of different types attractors in the system, such as, coexistence of two periodic attractors, coexistence of a periodic one and a quasi-periodic one, coexistence of a dual-wing chaotic one and a hyper-chaotic one, coexistence of two dual-wing chaotic ones, coexistence of a dual-wing chaotic one and a four-wing chaotic one, coexistence of two dual-wing hyper-chaotic ones, coexistence of two dual-wing quasi-periodic ones, coexistence of four attractors including two dual-wing hyper-chaotic ones, a four-wing chaotic one and a four-wing hyper-chaotic one; the simulation results of the system’s digital circuit and analog circuit are consistent to numerical analysis ones to reveal the system’s realizability; the system has high complexity in chaotic state and hyper-chaotic one, and its hyper-chaotic sequences pass 15 random tests specified in SP800-22 Revla.
Key words
hyper-chaotic system /
multi-stability /
multi-wing attractor /
circuit simulation
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