Existence and global exponential stability of anti-periodic solutions for delayed quaternion-valued cellular neural networks with impulsive effects
Existence and global exponential stability of anti-periodic solutions for delayed quaternion-valued cellular neural networks with impulsive effects
复制标题
具有脉冲效应的延迟四元值细胞神经网络反周期解的存在性和全局指数稳定性
DOI：
10.1002/mma.5318
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发表时间：
2019
影响因子：
2.9
通讯作者：
Bing Li
中科院分区：
文献类型：
--
作者：
李永昆;Jiali Qin;Bing Li
在本文中，我们考虑了一类具有脉冲效应的延迟四元数值细胞神经网络（DQVCNN）。利用重合度理论中的一个新的延拓定理，在激活函数有界的条件下，得到了DQVCNN反周期解的存在性.此外，通过构造合适的李雅普诺夫函数，推导出了保证DQVCNN反周期解全局指数稳定的一些充分条件。我们的结果是新的和补充的已知结果，即使当DQVCNN退化到真实的值或复值神经网络。最后通过一个例子说明了所得结果的有效性。
In this paper, we consider a class of delayed quaternion‐valued cellular neural networks (DQVCNNs) with impulsive effects. By using a novel continuation theorem of coincidence degree theory, the existence of anti‐periodic solutions for DQVCNNs is obtained with or without assuming that the activation functions are bounded. Furthermore, by constructing a suitable Lyapunov function, some sufficient conditions are derived to guarantee the global exponential stability of anti‐periodic solutions for DQVCNNs. Our results are new and complementary to the known results even when DQVCNNs degenerate into real‐valued or complex‐valued neural networks. Finally, an example is given to illustrate the effectiveness of the obtained results.