Abstract
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.
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