Constructing chaotic map with multi-cavity

Based on a simplified model, the methods and rules for generating multi-cavity chaotic map are presented. On this basis, a new rhombic cavity hyperchaotic map is constructed. Some typical dynamic properties of the new system are investigated, including phase trace, Lyapunov exponent spectrum (LEs) and bifurcations. The results show that the new chaotic map has rich dynamical behaviors, including complicated phase space trajectory, hyperchaotic behavior, large Lyapunov exponent. By changing the system parameters, the rhombic cavity with adjustable size and number are obtained. The rhombic cavity hyperchaotic map is improved to the multi-directional mode which has more complex topological structure than the original system. The complexity of the improved system is high at the entire parameter space. To verify the validity of the model and the feasibility of the systems, the digital circuits of the rhombic cavity hyperchaotic maps are implemented based on DSP technique. This lays a foundation for the application of these hyperchaotic maps in chaotic secure communication.