Abstract
In this study, we investigate reaction-diffusion complex-valued neural networks with mixed delays. The mixed delays include both time-varying and infinite distributed delays. Criteria are derived to ensure the existence, uniqueness, and exponential stability of the equilibrium state of the addressed system on the basis of the M-matrix properties and homeomorphism mapping theories as well as the vector Lyapunov function method. The results demonstrate the positive effect of reaction-diffusion on the stability, which further improves the existing conditions. Finally, the analysis of several examples is compared to the present results to verify the correctness and reduced conservatism of the primary results.
Highlights
1 Introduction Because there are many potential applications of CVNNs [1,2,3,4], there has been increasing interest in research and development related to complex-valued neural networks (CVNNs), in which neuron states and connection matrices are defined in the complex number domain
It is noteworthy that the results proposed in [30,31,32,33,34,35,36,37,38,39,40,41,42] and the references therein only work for real-valued neural networks (RVNNs)
5 Conclusions and future research A type of reaction-diffusion CVNNs (RDCVNNs) with time-varying and infinite distributed delays was investigated in this study
Summary
Because there are many potential applications of CVNNs [1,2,3,4], there has been increasing interest in research and development related to complex-valued neural networks (CVNNs), in which neuron states and connection matrices are defined in the complex number domain. The major contributions of this study are: (1) models of RDCVNNs with mixed delays are considered, which include related existing models; (2) a new lemma is proposed to process the reaction-diffusion terms of NNs, which demonstrates a stronger positive influence of the reaction-diffusion terms on stability than that of the lemmas in [32, 36, 37, 40]; (3) by adopting the vector Lyapunov function method combined with the M-matrix properties and the homeomorphism mapping theory, some sufficient conditions without any relax variables are established for ensuring the existence, uniqueness, and global exponential stability of the equilibrium state of the proposed system; (4) the established stability conditions exhibit compacted matrix forms, which do not depend on an individual attempt; and (5) several numerical examples are provided to demonstrate the feasibility and lower-level conservatism of the established results as compared with the previously existing ones.
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