Multistability Analysis, Coexisting Multiple Attractors, and FPGA Implementation of Yu-Wang Four-Wing Chaotic System

Abstract

In this paper, we further study the dynamic characteristics of the Yu-Wang chaotic system obtained by Yu and Wang in 2012. The system can show a four-wing chaotic attractor in any direction, including all 3D spaces and 2D planes. For this reason, our interest is focused on multistability generation and chaotic FPGA implementation. The stability analysis, bifurcation diagram, basin of attraction, and Lyapunov exponent spectrum are given as the methods to analyze the dynamic behavior of this system. The analyses show that each system parameter has different coexistence phenomena including coexisting chaotic, coexisting stable node, and coexisting limit cycle. Some remarkable features of the system are that it can generate transient one-wing chaos, transient two-wing chaos, and offset boosting. These phenomena have not been found in previous studies of the Yu-Wang chaotic system, so they are worth sharing. Then, the RK4 algorithm of the Verilog 32-bit floating-point standard format is used to realize the autonomous multistable 4D Yu-Wang chaotic system on FPGA, so that it can be applied in embedded engineering based on chaos. Experiments show that the maximum operating frequency of the Yu-Wang chaotic oscillator designed based on FPGA is 161.212 MHz.