Design and FPGA implementation of multi-wing chaotic switched systems based on a quadratic transformation* *Project supported by the National Natural Science Foundation of China (Grant Nos. 61973199 and 61973200) and the Taishan Scholar Project of Shandong Province of China.

Abstract

Based on a quadratic transformation and a switching function, a novel multi-wing chaotic switched system is proposed. First, a 4-wing chaotic system is constructed from a 2-wing chaotic system on the basis of a quadratic transformation. Then, a switching function is designed and by adjusting the switching function, the number and the distribution of the saddle-focus equilibrium points of the switched system can be regulated. Thus, a set of chaotic switched systems, which can produce 6-to-8-12-16-wing attractors, are generated. The Lyapunov exponent spectra, bifurcation diagrams, and Poincaré maps are given to verify the existence of the chaotic attractors. Besides, the digital circuit of the multi-wing chaotic switched system is designed by using the Verilog HDL fixed-point algorithm and the state machine control. Finally, the multi-wing chaotic attractors are demonstrated via FPGA platform. The experimental results show that the number of the wings of the chaotic attractors can be expanded more effectively with the combination of the quadratic transformation and the switching function methods.