A Novel Method for Constructing Grid Multi-Wing Butterfly Chaotic Attractors via Nonlinear Coupling Control

Yun Huang

doi:10.1155/2016/9143989

Abstract

A new method is presented to construct grid multi-wing butterfly chaotic attractors. Based on the three-dimensional Lorenz system, two first-order differential equations are added along with one linear coupling controller, respectively. And a piecewise linear function, which is taken into the linear coupling controller, is designed to form a nonlinear coupling controller; thus a five-dimensional chaotic system is produced, which is able to generate gird multi-wing butterfly chaotic attractors. Through the analysis of the equilibrium points, Lyapunov exponent spectrums, bifurcation diagrams, and Poincaré mapping in this system, the chaotic characteristic of the system is verified. Apart from the research above, an electronic circuit is designed to implement the system. The circuit experimental results are in accordance with the results of numerical simulation, which verify the availability and feasibility of this method.

Highlights

Since Lorenz found the first chaotic model in 1963 [1], people have had a great interest to construct the chaotic attractors with different shape and quantity
The existing chaotic attractors could be divided into two types: the multiscroll chaotic attractors and the multi-wing butterfly chaotic attractors
Reference [17] constructed a class of hyperchaotic systems generating 2n-wing butterfly hyperchaotic attractors by coordinate transition and absolute value transition

Summary

Introduction

Since Lorenz found the first chaotic model in 1963 [1], people have had a great interest to construct the chaotic attractors with different shape and quantity. By designing some piecewise functions to take place of the state variables of the Lorenz system directly, [20, 22] proposed some multi-wing and grid multi-wing butterfly chaotic systems. Through combining a linear coupling controller with a piecewise linear function skillful, a new method is presented to construct grid multi-wing butterfly chaotic attractors. A piecewise linear function, which is taken into the linear coupling controller, is designed to form a nonlinear coupling controller; a five-dimensional chaotic system is produced, which is able to generate gird multi-wing butterfly chaotic attractors. 2. Constructing the Grid Multi-Wing Butterfly Chaotic Attractors via the Nonlinear Coupling Control. Constructing grid multi-wing butterfly chaotic attractors via the nonlinear coupling control, the method is shown as follows.

Basic Dynamic Characteristic

Circuit Design of the Grid Multi-Wing Butterfly Chaotic Attractors

Conclusion