Two-Dimensional Bounded Chaotic System With Hardware Implementation

Designing low-dimensional hyperchaotic (HC) maps with high randomness and controllable dynamic amplitude is greatly important but also extremely challenging. To overcome the shortcomings of existing two-dimensional (2-D) maps, this article proposes a unified mapping framework for constructing 2-D bounded chaotic system (2D-BCS) with provable boundedness. To prove its validity, eight examples of 2-D bounded hyperchaotic maps (2D-BHMs) are provided by combining three bounded functions. Taking specific 2D-BHMs as examples, we investigate the bifurcation and coexisting behaviors under small parameters, and the robust HC dynamics and performance indicators under large parameters. Numerical results manifest that these maps exhibit controllable dynamic amplitude, ultrawide parameter space, and high-performance indicators. These maps are implemented on STM32 hardware platform, and the experimental results are obtained to verify the numerical results. Additionally, two pseudorandom number generators (PRNGs) are developed to explore potential applications of 2D-BHMs. NIST test results demonstrate that our PRNGs can provide binary sequences with high randomness.