A Sine-coupled model for constructing N-dimensional non-degenerate discrete hyperchaotic map

Abstract

The non-degenerate hyperchaotic systems with the maximum number of positive Lyapunov exponents (LEs) typically have better ergodicity, pseudo randomness, and stronger anti-degeneration property. Therefore, designing non-degenerate hyperchaotic maps with complex dynamics has attracted increasing attention from various research fields in recent years. By introducing the sine function, this paper proposes a construction model of N-dimensional non-degenerate discrete hyperchaotic map. To verify the effectiveness of this model, we provide three sub-maps of different dimensions based on this model as illustrative examples, and the dynamic behavior is explored using multiple numerical measures. The results demonstrate that the sub-maps with concise symmetric structures have complex dynamics, such as ultra-wide non-degenerate hyperchaotic parameter range, state transition phenomenon, and multistability. In particular, coexisting symmetric attractors and quasi-periodic curves switch periodically with the change of initial value. Furthermore, the hyperchaotic sequences generated by the three sub-maps have excellent performance, and the NIST test also further verifies the super randomness and unpredictability of these sequences. Finally, through the DSP hardware platform, the physical realizability of the sub-maps is verified successfully.