Li Ke, Cao Jianxiong, He Jin-Man
School of Electronic Information and Electrical Engineering, Tianshui Normal University, Tianshui 741000, China.
School of Sciences, Lanzhou University of Technology, Lanzhou 730050, China.
Chaos. 2020 Mar;30(3):033129. doi: 10.1063/1.5136057.
The research of finding hidden attractors in nonlinear dynamical systems has attracted much consideration because of its practical and theoretical importance. A new fractional order four-dimensional system, which can exhibit some hidden hyperchaotic attractors, is proposed in this paper. The predictor-corrector method of the Adams-Bashforth-Moulton algorithm and the parameter switching algorithm are used to numerically study this system. It is interesting that three different kinds of hidden hyperchaotic attractors with two positive Lyapunov exponents are found, and the fractional order system can have a line of equilibria, no equilibrium point, or only one stable equilibrium point. Moreover, a self-excited attractor is also recognized with the change of its parameters. Finally, the synchronization behavior is studied by using a linear feedback control method.
由于其实际和理论重要性，在非线性动力系统中寻找隐藏吸引子的研究受到了广泛关注。本文提出了一个新的分数阶四维系统，该系统能够展现出一些隐藏的超混沌吸引子。采用亚当斯-巴什福思-莫尔顿算法的预估-校正方法和参数切换算法对该系统进行数值研究。有趣的是，发现了具有两个正李雅普诺夫指数的三种不同类型的隐藏超混沌吸引子，并且分数阶系统可以有一条平衡点线、没有平衡点或只有一个稳定平衡点。此外，随着参数的变化还识别出了一个自激吸引子。最后，利用线性反馈控制方法研究了同步行为。
