Combining conformable differential definition and Adomian decomposition method (ADM) algorithm, the dynamics of a new 4-D fractional-order chaotic system was studied through numerical simulation in this paper. The dissipation of the system and the stability of the equilibrium points were analyzed. The evolution of the coexistence attractors with different parameters and orders were analyzed through the coexistence bifurcation diagrams, coexistence Lyapunov exponent spectrums and coexistence phase diagrams. In addition, the 0–1 test is used as an auxiliary method to verify the attractor status of the system. It is novel to use the attraction basin to investigate the dynamic behaviors of the system when two parameters change at the same time. Moreover, the digital signal processing (DSP) technology was used to simulate the fractional-order chaotic system on digital circuits, and the results are consistent with numerical simulation on computer. This research provides theoretical basis and guidance for the applications and teaching of fractional-order chaotic systems.

本文通过数值模拟的方法，将符合差分定义和Adomian分解方法（ADM）算法相结合，研究了一种新的4-D分数阶混沌系统的动力学。分析了系统的耗散和平衡点的稳定性。通过共存分歧图，共生Lyapunov指数谱和共存相图，分析了不同参数和阶数的共存吸引子的演化。另外，将0-1测试用作辅助方法来验证系统的吸引子状态。当两个参数同时变化时，使用吸引盆研究系统的动态行为是一种新颖的方法。此外，利用数字信号处理（DSP）技术对数字电路中的分数阶混沌系统进行了仿真，其结果与计算机数值模拟相吻合。本研究为分数阶混沌系统的应用和教学提供理论依据和指导。