Design And Circuit Implementation Of Multi-scroll Chaotic System Based On Asymmetric Double-scroll System

Abstract:In recent30years, domestic and international researchers have made many important achievements in chaotic area. Especially in modeling multi-scroll chaotic system, many scholars have proposed new chaotic system models, and introduced a variety of multi-scroll chaotic attractor generated methods and hardware implementation technologies. However, all existing multi-scroll chaotic systems are generated based on the double-scroll system, nobody find an asymmetric system can generate multi-scroll attractors so far.This paper researches the design and implementation of multi-scroll chaotic system based on an asymmetric system according to the chaos theory and technology of computer simulation.Firstly, a new simple third-order asymmetric chaotic system, which only contains one nonlinear term and three design parameters, is proposed. We demonstrated that the system is chaotic by analyzing the stability of system equilibrium points, calculating Lyapunov exponents, and drawing bifurcation diagram. Then, MATLAB is used to perform the numerical simulation of the system. Simulation results show that the system has chaotic characteristics.Next, the third-order system becomes an asymmetric double-scroll system by improving the third-order asymmetric chaotic system, which includes adding a simple sawtooth function to the system, and readjusting each parameter value. The original system becomes an asymmetric double-scroll system. Then, we design the analog electronic circuit of the new system by using the improved module-based method, and observe the phase plane chaotic attractors by employing EWB simulation. The results are consistent with the theoretical analysis.Then, we propose a method of generating single-direction distribution multi-scroll chaotic attractors based on the asymmetric double-scroll system. Meantime, the asymmetric system can generate multi-scroll chaotic attractors by using sawtooth function series to extend the index-2saddle-focus point. The nonlinear function circuit and the system main circuit are designed for two examples of10-scroll (even number) and9-scroll (odd number), respectively. EWB simulation results show the feasibility of this method.