A novel 3D non-degenerate hyperchaotic map with ultra-wide parameter rang and coexisting attractors periodic switching

Abstract With the maximum number of positive Lyapunov exponents, the non-degenerate hyperchaotic systems typically have more complex dynamics and better anti-degradation properties than general chaotic systems. By introducing trigonometric functions, this paper proposes a three-dimensional(3D) hyperchaotic map with a concise symmetric structure. From the perspective of the Lyapunov exponent, it is proved mathematically that the new map can always maintain the chaotic state in an infinitely wide parameter range. Numerical simulations further show that the map has rich dynamic behaviors, such as antimonotonicity, transient chaos, and coexisting symmetric attractors. In particular, periodic switching of symmetric attractors can be achieved by changing the initial value, which is rarely seen in other chaotic maps. Furthermore, combined with an offset constant, the polarity transformation of the attractors in a single direction has been realized successfully. Finally, the performance analysis indicates that the sequence generated by the new map has extremely higher complexity and pseudo-randomness, and the physical realizability of the map is also verified by the results of the DSP hardware experiment.