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...

中文翻译：

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相容分数阶混沌系统的多稳定性分析

提出了一种结合分数阶导数和CADM算法的分数阶混沌系统新算法，并将其应用于分数阶Jerk混沌系统。分析了系统平衡点的耗散性和稳定性。通过分岔图的共存，Lyapunov指数谱的共存，吸引子的共存图，引力池和初值动力学图，分析了系统参数和阶数对分数阶新的Jerk混沌系统动力学行为的影响。该系统具有丰富的动态特性。首先，该系统至少具有12个形状不同的混沌吸引子。当传统参数和顺序被视为分叉控制参数时，会出现多种共存的分叉行为和多个吸引子的共存。更有趣的是，吸引子并存，并且不同状态下的多状态转换。