具有时变时滞的Cohen-Grossberg神经网络的广义同步
Cohen-Grossberg Neural Networks with Time-Varying Delays Generalized Synchronization
摘要: 本文利用辅助系统方法研究了一类具有时变时滞的Cohen-Grossberg型神经网络的广义同步问题。首先，基于李雅普诺夫稳定性理论，得到了保证响应系统和辅助系统之间实现指数同步的充分条件。其次，利用线性矩阵不等式，得到了响应系统和辅助系统有限时间混合外同步的充分条件。随后，根据辅助系统方法得出驱动系统与响应系统广义同步。上述结果同样适用于延迟细胞神经网络，结果具有一般性。最后，给出相应的数值模拟来验证所得结论的有效性。
Abstract: This paper investigates the generalized synchronization problem of a class of Cohen-Grossberg type neural networks with time-varying delays using the auxiliary system method. Firstly, based on Lyapunov stability theory, sufficient conditions are obtained to ensure exponential synchronization between the response system and the auxiliary system. Secondly, using linear matrix inequality, sufficient conditions for finite time mixed external synchronization between the response system and the auxiliary system are obtained, According to the auxiliary system method, the generalized synchronization between the driving system and the response system is obtained. The above re-sults are also applicable to delayed cellular neural networks, and the results are general. Finally, corresponding numerical simulations are provided to verify the effectiveness of the obtained con-clusions.
文章引用：李疏桐, 蔡旭颖, 胡湘涵, 李婷, 张川. 具有时变时滞的Cohen-Grossberg神经网络的广义同步[J]. 应用数学进展, 2024, 13(2): 832-847. https://doi.org/10.12677/AAM.2024.132080

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