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

Based on trigonometric functions, we propose a three-dimensional (3D) hyperchaotic map with a concise symmetric structure. From the perspective of Lyapunov exponents, we establish the mathematical proof that the new map consistently maintains a chaotic state across an infinitely wide parameter range. Numerical simulations illuminate a diverse array of dynamic behaviors, including an ultra-wide range of non-degenerate hyperchaotic parameters, antimonotonicity, transient chaos, and multiple coexisting attractors. Particularly noteworthy, altering initial values enables the periodic switch of symmetric attractors-a rare phenomenon within other chaotic maps. Moreover, in conjunction with an offset constant, successful polarity transformation of attractors in a single direction has been achieved. Furthermore, performance analysis underscores that the sequence generated by the new map embodies significantly elevated complexity and pseudo-randomness. Finally, we implement the new map using a digital signal processing platform and successfully validate its physical feasibility by obtaining the chaotic attractors.