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

Abstract EN

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.