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.

中文翻译：

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新的4D分数阶系统中的隐藏超混沌吸引子及其同步

在非线性动力学系统中寻找隐藏吸引子的研究由于其实际和理论意义而引起了广泛的关注。本文提出了一个新的分数阶四维系统，该系统可以表现出一些隐藏的超混沌吸引子。使用Adams–Bashforth–Moulton算法的预测器-校正器方法和参数切换算法对系统进行了数值研究。有趣的是，发现了具有两种正Lyapunov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具有一条平衡线，没有平衡点或只有一个稳定平衡点。而且，自激吸引子也随着其参数的变化而被识别。最后，