Memristor-Based Hyperchaotic Maps and Application in AC-GANs

With the nonlinearity and plasticity, memristors are widely used as nonlinear devices for chaotic oscillations or as biological synapses for neuromorphic computations. But discrete memristors and their coupling maps have not received much attention, yet. Using a discrete memristor model, this paper presents a general three-dimensional discrete memristor-based (3D-DM) map model. By coupling the discrete memristor with four two-dimensional discrete maps, four examples of 3D-DM maps with no or infinitely many fixed points are generated. We simulate the coupling coefficient-depended and memristor initial-boosted bifurcation behaviors of these 3D-DM maps using numerical measures. The results demonstrate that the memristor can enhance the chaos complexity of existing discrete maps and its coupling maps can display hyperchaos. Furthermore, a hardware platform is developed to implement the 3D-DM maps and the acquired hyperchaotic sequences have high randomness. Particularly, these hyperchaotic sequences can be applied to the auxiliary classifier generative adversarial nets (AC-GANs) for greatly improving the discriminator accuracy.