Hybrid tri-memristor hyperchaotic map and application in Wasserstein Generative Adversarial Nets

Inspired by basic circuit connection methods, memristors can also be utilized in the construction of complex discrete chaotic systems. To investigate the dynamical effects of hybrid memristors, we propose two hybrid tri-memristor hyperchaotic (HTMH) mapping structures based on the hybrid parallel/cascade and cascade/parallel operations, respectively. Taking the HTMH mapping structure with hybrid parallel/cascade operation as an example, this map possesses a spatial invariant set whose stability is closely related to the initial states of the memristors. Dynamics distributions and bifurcation behaviours dependent on the control parameters are explored with numerical tools. Specifically, the memristor initial offset-boosting mechanism is theoretically demonstrated, and memristor initial offset-boosting behaviours are numerically verified. The results clarify that the HTMH map can exhibit hyperchaotic behaviours and extreme multistability with homogeneous coexisting infinite attractors. In addition, an FPGA hardware platform is fabricated to implement the HTMH map and generate pseudorandom numbers (PRNs) with high randomness. Notably, the generated PRNs can be applied in Wasserstein generative adversarial nets (WGANs) to enhance training stability and generation capability.