Topological Horseshoe Analysis, Ultimate Boundary Estimations of a New 4D Hyperchaotic System and Its FPGA Implementation

Abstract

This paper constructs a new four-dimensional (4D) hyperchaotic system. Firstly, the influence of parameter variation on the dynamic behavior of the system is analyzed in detail using Lyapunov exponents and the bifurcation diagram. Additionally, the topological horseshoe finding algorithm is based on three-dimensional (3D) hyperchaotic mapping. Through searching for the 3D topological horseshoe with two-dimensional stretching on the Poincaré section, the existence of the 4D hyperchaotic system is proved in the mathematical sense. Next, Lyapunov stability theory and optimization method are used to further analyze the ultimate boundary of the proposed 4D hyperchaotic system. Thus, the 3D ellipsoidal boundary of the hyperchaotic system is found. Finally, this paper also takes the hyperchaotic system as an example and presents the experimental results of generated hyperchaotic attractors by FPGA technology. The experimental results show that the phase diagram of hyperchaotic system is consistent for the simulated results. Due to the more complex dynamic behavior, the proposed system is suitable for engineering application, such as in chaotic secure communications.