Generalized synchronization is a typical dynamical phenomenon in nonlinear systems, for which the real-valued setting has been widely investigated. The complex-valued functions relationship in generalized synchronization is equally important for complex-valued dynamical systems, which however are seldom studied. Complex parameters identification on the synchronization manifold remains an open problem owing to the absence of the persistent excitation (PE) condition in the complex field. This paper investigates generalized synchronization via a complex-valued vector mapping (CGS) for different-dimensional complex-variable chaotic (hyper-chaotic) systems (CVCSs) with complex parameters identification. Based on Lyapunov stability theory in the complex field and using an adaptive control method, some sufficient criteria are established to achieve CGS for CVCSs. Moreover, some necessary and sufficient criteria are derived to ensure complex parameters identification. Finally, the theoretical results are verified and demonstrated by reduced-order and increased-order simulation examples.

中文翻译：

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复杂场中多维混沌系统的广义同步与参数识别

广义同步是非线性系统中的典型动力学现象，实值设置已被广泛研究。广义同步中的复值函数关系对于复值动力系统同样重要，但很少被研究。由于复杂场中不存在持续激励（PE）条件，同步流形上的复杂参数识别仍然是一个悬而未决的问题。本文通过复值向量映射 (CGS) 研究了具有复杂参数识别的不同维复变量混沌（超混沌）系统 (CVCS) 的广义同步。基于复场李雅普诺夫稳定性理论，采用自适应控制方法，建立了一些充分的标准来实现 CVCS 的 CGS。此外，导出了一些必要和充分的标准，以确保复杂的参数识别。最后，通过降阶和增阶仿真实例对理论结果进行了验证和论证。