In this paper, a three-dimensional nonlinear system with only one equilibrium point is constructed based on the Anishchenko-Astakhov oscillator. The system is analyzed in detail using time-domain waveform plots, phase diagrams, bifurcation diagrams, Lyapunov exponent spectra, basins of attraction, spectral entropy, and C₀ complexity (a parameter for dynamic properties). It is found that this system has excellent dynamical behavior: the emergence of novel multiple shapes of two-channel attractors and the gradual evolution of clumped and ring-shaped attractors can be tuned by only one parameter. The system also exhibits multistability with three types of dynamical behavior, namely, coexistence of two types of periodic attractors, and coexistence of quasi-periodic/chaotic attractors at different initial values. Moreover, the system has transient behavior, significantly increasing the complexity of the system. Finally, a hardware circuit mimicking the system is implemented. Such dynamical characteristics can be controlled by only one parameter, which is great cost savings and highly efficient in engineering applications.

本文基于Anishchenko-Astakhov振子构造了一个只有一个平衡点的三维非线性系统。使用时域波形图、相图、分岔图、 Lyapunov 指数谱、吸引力盆地、谱熵和 C _{0对系统进行了详细分析}复杂性（动态属性的参数）。发现该系统具有优异的动力学行为：新的多种形状的双通道吸引子的出现以及团块和环形吸引子的逐渐演变可以仅通过一个参数进行调整。该系统还表现出具有三种动力学行为的多稳定性，即两种类型的周期性吸引子共存，以及不同初始值的准周期/混沌吸引子共存。此外，系统具有瞬态行为，显着增加了系统的复杂性。最后，实现了模拟系统的硬件电路。这样的动态特性可以通过一个参数来控制，这在工程应用中可以节省大量成本和高效。