Design and implementation of a heterogeneous multi-cavity hyperchaotic map derived from complex exponential functions

To enhance the structural complexity of multi-cavity chaotic maps, a new complex exponential chaotic map (CECM) is proposed based on complex exponential functions. Its attractor shape is sensitive to parameters. By integrating the CECM with step functions, a heterogeneous multi-cavity hyperchaotic map (HMCM) is created that generates multiple cavities with unique structures, enhancing system complexity. Dynamical analyses, including attractor phase diagram, Lyapunov exponents, and permutation entropy complexity, verify the hyperchaotic performance across a wide parameter range. The HMCM is implemented on a digital signal processor platform, performing on-chip computations of the bifurcation diagram and Lyapunov exponents. The integrated hardware analysis confirms the physical feasibility, robust chaos, and low-resource usage of the map.