In this paper, the stabilization and synchronization of a complex hidden chaotic attractor is shown. This article begins with the dynamic analysis of a complex Lorenz chaotic system considering the vector field properties of the analyzed system in the ${\mathbb{C}}^n$ domain. Then, considering first the original domain of attraction of the complex Lorenz chaotic system in the equilibrium point, by using the required set topology of this domain of attraction, one hidden chaotic attractor is found by finding the intersection of two sets in which two of the parameters, r and b, can be varied in order to find hidden chaotic attractors. Then, a backstepping controller is derived by selecting extra state variables and establishing the required Lyapunov functionals in a recursive methodology. For the control synchronization law, a similar procedure is implemented, but this time, taking into consideration the error variable which comprise the difference of the response system and drive system, to synchronize the response system with the original drive system which is the original complex Lorenz system.

中文翻译：

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复杂隐吸引子混沌系统的反步法稳定与同步

在本文中，展示了复杂隐藏混沌吸引子的稳定和同步。本文首先对复杂洛伦兹混沌系统进行动态分析，考虑到所分析系统的矢量场特性${\mathbb{C}}^n$领域。然后，首先考虑平衡点上复杂洛伦兹混沌系统的原始吸引力域，通过使用该吸引力域所需的集合拓扑，通过找到两个集合的交集，找到一个隐藏的混沌吸引子，其中两个集合参数，r和b, 可以变化以找到隐藏的混沌吸引子。然后，通过选择额外的状态变量并以递归方法建立所需的李雅普诺夫函数，推导出一个反推控制器。对于控制同步律，实现了类似的过程，但这次考虑到包含响应系统和驱动系统差异的误差变量，将响应系统与原始复杂洛伦兹驱动系统同步系统。