两个具有耦合时滞的分数阶复杂网络的延迟投影同步与参数辨识
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空军工程大学

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TP273

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Lag projective synchronization and parameter identification of two fractional-order complex networks with coupling delay
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Air Force Engineering University

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    摘要:

    本文研究了两个具有耦合时滞的分数阶复杂网络的延迟投影同步与参数辨识的问题。首先建立了具有耦合时滞以及模型参数不确定分数阶复杂网络模型,并给出了驱动网络与响应网络的延迟投影同步误差模型。其次设计了有效的控制器以及参数自适应律以实现两个网络之间的延迟投影同步与参数辨识,给出了实现延迟投影同步与参数辨识的充分条件,对该充分条件给出了严格的数学证明。并通过一个数值仿真实例验证了文中提出方法的有效性和可行性。然后,还对文中三种特例进行了讨论,并得到了实现同步的充分条件,这三种情况分别为具有耦合时滞的延迟同步、具有耦合时滞的投影同步和没有耦合时滞的延迟投影同步,说明本文的研究更具有普遍性。最后,讨论了模型中耦合强度,时滞因素,以及投影比例对同步的影响。

    Abstract:

    In this paper, the problem of lag projection synchronization and parameter identification for two fractional-order complex networks with coupled delays is investigated. Firstly, the fractional-order complex network model with coupling delay and uncertain parameters is established, and the lag projection synchronization error model of the driving network and the response network is given. Secondly, the effective controller and the parameter adaptive law are designed to realize lag projection synchronization and parameter identification between the two networks. A sufficient condition for realizing lag projection synchronization and parameter identification is given, and a strict mathematical proof is given for this sufficient condition. The validity and feasibility of the proposed method are verified by a numerical simulation example. Then, three special cases are discussed and sufficient conditions are obtained to realize synchronization, which are lag synchronization with coupled time delay, projection synchronization with coupled time delay and lag projection synchronization without coupled time delay, indicating that the study in this paper is more general. Finally, the effects of coupling strength, time-delay, and projection ratio are discussed.

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历史
  • 收稿日期:2020-08-24
  • 最后修改日期:2021-03-26
  • 录用日期:2021-03-29
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