Complexity enhancement and grid basin of attraction in a locally active memristor-based multi-cavity map

Abstract

The complexity of memristive chaotic systems determines whether it is suitable for applications in different subjects. To enhance complexity both in performance and diversity, this article first proposes a discrete model of locally active memristor (LAM) and conceives a three-dimensional memristive multi-cavity map by coupling LAM with the existing sine and cosine modulation (SCM) map. This map is named LAM-SCM map and has numerous independent fixed points with different stabilities. Numerical simulations reveal the memristive parameters-relied lossless displacement and self-shift of multi-cavity attractors, indicating the dynamical effects of LAM on the existing SCM map. The initial-relied dynamics distributions are disclosed by grid basins of attraction, showing the emergence of initial-boosting coexistence. Besides, the performance comparisons verify the superiority of LAM-SCM map over the existing SCM map. Finally, a hardware platform has been developed on FPGA to implement the LAM-SCM map and the captured attractors validate the numerical results. On this basis, we devise a 32-bit pseudorandom number generator (PRNG) based on chaos and implement it on the FPGA-based hardware platform to obtain high-speed and reconfigurable pseudorandom numbers. The results show that the proposed map has enhanced chaos complexity and rich dynamics diversity, which ensures the availability of hardware PRNG.