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Existence and global exponential stability of anti‐periodic solutions for delayed quaternion‐valued cellular neural networks with impulsive effects
Author(s) -
Li Yongkun,
Qin Jiali,
Li Bing
Publication year - 2018
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5318
Subject(s) - mathematics , quaternion , bounded function , lyapunov function , exponential stability , coincidence , degenerate energy levels , stability (learning theory) , artificial neural network , cellular neural network , class (philosophy) , control theory (sociology) , mathematical analysis , pure mathematics , nonlinear system , computer science , medicine , physics , geometry , alternative medicine , control (management) , pathology , quantum mechanics , machine learning , artificial intelligence
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.