Multistability analysis of a conformable fractional-order chaotic system

Abstract

In this paper, a new algorithm which is combined conformable fractional derivative and CADM algorithm for solving fractional-order chaotic system is proposed and applied to a new fractional-order Jerk chaotic system. The dissipative and stability of equilibrium points of the system are analyzed. The influences of system parameters and order on the dynamic behaviors of the fractional-order new Jerk chaotic system are analyzed by coexistence of bifurcation diagrams, coexistence of Lyapunov exponent spectrums, attractors coexisting diagrams, attraction basin and dynamics map for initial values. The system exhibits rich dynamic characteristics. Firstly, the system has at least 12 chaotic attractors with different shapes. Multifarious coexistence bifurcation behaviors and coexistence of multiple attractors appear when the traditional parameters and order treated as bifurcation control parameters. More interestingly, attractors coexisting, and multiple state transition under different parameters and orders are analyzed. The result shows that the fractional-order new Jerk chaotic system has rich dynamics characteristics. In addition, the fractional chaotic sequences are generated by DSP, and the results are consistent with numerical simulation. The research results provide guidance for the application and teaching of the conformable fractional-order new Jerk chaotic system.