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.