Design Of Multi-scroll Chaotic Attractors Through General Hysteresis Function And Its Circuit Implementation

Chaos has been found in nature and the physical sciences since the last century.Many research results have been applied in many disciplines such as engineering control,confidential communications,social economy,and life sciences.Constructing novel chaotic systems and applying them to different fields is one of the many research hotspots.Multi-scroll chaotic system is a novel chaotic system,which has received extensive attention due to its complex dynamic characteristics.At present,they have the following characteristics.First,the size of a single scroll in a multi-scroll chaotic attractor is nearly same.Secondly,attractors are arranged in a single way,mostly in one-dimensional linear and two-dimensional grid distribution.Its dynamic behavior is relatively simple,which restricts the application of chaotic systems.In order to solve the above problems,the improved hysteresis function is used as a nonlinear switching function to generate novel nested and L-shaped multi-scroll chaotic attractors which have more complex dynamic behaviors.Not only it enriches the construction method of multi-scroll chaotic attractor,it also makes the multi-scroll chaotic system more widely used.The main work of this paper is as follows.1.The classical symmetric hysteresis function is improved to general hysteresis function which has different output value magnitudes and state numbers in the process of increasing and decreasing the independent variables.Then,the improved hysteresis function is used as the nonlinear switching function of the three-dimensional spiral system to construct the nested and L-shaped scroll chaotic systems.The formation process of chaotic attractors is illustrated by analyzing the switching principle between system equilibrium points.By using MATLAB,the formation process of chaotic attractors is illustrated by analyzing the switching principle between system equilibrium points.2.Based on the constructed differential equations of nested and L-shaped multiscroll chaotic systems,its actual circuits are designed.The design idea of circuit module is described in detail,and the branch circuit of each component is designed by using the proportional circuit module of reverse addition and subtraction,integral and reverse circuit module.The circuit of the whole chaotic system is realized by orderly connecting the respective branch circuits through input and output relationships.The system circuit is designed by using the MULTISIM software,and the hardware physical circuit board is fabricated.By observing the chaotic attractor image through the oscilloscope,the results are basically consistent with the MATLAB simulation which proves the achievability of the design methods of the nested and L-shaped attractor.