Fractional-order multiwing switchable chaotic system with a wide range of parameters

Abstract

This paper presents a novel fractional-order multiwing switchable Liu chaotic system by introducing a state equation. Multiwing switching can be realized by switching the new equation coefficient symbols with symbolic functions. The new fractional-order multiwing switchable Liu chaotic system has various switching branches, a simple construction method, and an outstanding performance effect. On this basis, by modifying the nonlinear term of the equation, a new fractional-order chaotic system with variable powers of the nonlinear term and a wide range of value parameters is constructed. The dynamic characteristics of the new system are studied through theoretical numerical simulation, such as phase diagrams, equilibrium points, the multiwing generation mechanism, Lyapunov exponent spectra and Poincare cross-section. The Poincare cross-section diagrams are used to compare and analyze the power change of the nonlinear term and the wide range of parameter values in the new system. Furthermore, the method of constructing the fractional-order multiwing switchable system is applied to the fractional-order Lorenz, Chen, and Lü systems. Finally, a Multisim chaotic circuit of the fractional-order multiwing Liu system is designed. The simulation results demonstrate that the construction method of the fractional-order multiwing switchable chaotic system is feasible and offers good generality.