Coexisting point attractors, multi-transient behaviors, area-preserving chaotic systems, non-degenerate hyperchaotic systems derived from a simple 3D discrete system

Abstract

In this paper, we propose a simple 3D discrete system with a variety of interesting dynamic behaviors. When the control parameters of the discrete system are set to different appropriate values, the system is transformed into four distinct systems, namely a discrete system with coexisting point attractors, a discrete system with novel multi-transient behaviors, an area-preserving map, and a non-degenerate hyperchaotic system. This transient transition behavior is manifested as a switch between multiple quasi-periodic flows. This multi-transient behavior is rarely reported in discrete systems. In addition, to meet the requirements of chaotic secure communication, relevant experiments prove that the pixel scrambling effect of the proposed area-preserving map is better than that of the 3D digital Arnold map. Moreover, a PRNG is constructed by quantizing the proposed non-degenerate hyperchaotic system, and the PRNG can pass the NIST SP-800-22 test and show good randomness.