Discrete memristive maps with multi-topology chaotic/hyperchaotic attractors and application in secure communication

Chaotic systems are extensively applied in secure communications because of their unpredictability, yet their noise resistance is often undermined by limited dynamical diversity and single attractor topology. To address this challenge, this paper proposes a novel discrete multi-topology chaotic/hyperchaotic memristive map (MTCHMM) based on a 2D threshold discrete map (2D-TDM). Under varying parameter settings, the MTCHMM can exhibit multi-attractors with distinctly different topological structures, including multi-note chaotic attractors, multi-top hyperchaotic attractors, multi-hourglass hyperchaotic attractors, and multi-diamond hyperchaotic attractors. Furthermore, increasing the initial offsets of the memristor enables the stable coexistence of different numbers of attractors, indicating that the MTCHMM displays homogeneous multistability. Notably, the output amplitude of the MTCHMM can achieve hyperchaotic modulation on an extensive scale via memristor-related parameters. Performance analysis indicates that the MTCHMM exhibits complex fractal structures and higher entropy values, thereby significantly enhancing its complexity and unpredictability. The physical feasibility of the MTCHMM is validated by hardware experiments on the STM32 platform. Finally, by combining the multi-topology attractors from the MTCHMM with the traditional DCSK scheme, a novel folded orthogonal DCSK (FO-DCSK) scheme is designed. Experimental results show that this scheme exhibits excellent noise resistance.