期刊信息
- 刊名： 河北师范大学学报（自然科学版）Journal of Hebei Normal University (Natural Science)
- 主办： 河北师范大学
- ISSN： 1000-5854
- CN： 13-1061/N
- 中国科技核心期刊
- 中国期刊方阵入选期刊
- 中国高校优秀科技期刊
- 华北优秀期刊
- 河北省优秀科技期刊
具混合时滞复值 Hopfield神经网络的渐进概周期解
- (云南大学 数学与统计学院,昆明 650091)
-
DOI：10.13763/j.cnkij.hebnu.nse.202501007
Asymptotically Almost Periodic Solutions of Complex-valued Hopfield Neural Networks with Mixed Time Delays
摘要/Abstract
研究了一类具混合时滞复值Hopfield神经网络的渐进概周期解的存在性.与以往多讨论实值神经网络的成果不同,考虑到实值Hopfield神经网络在问题处理过程中的局限性,提出复值网络是为了处理在实数域上不能直接处理的复值条件,同时当复值条件的虚部为0时,复值系统就可以直接处理实数数值.首先要将复数数据处理分成实部和虚部来讨论,利用Banach空间中的不动点定理、实数集上的指数二分性和若干微分方程不等式技巧,分别对实部和虚部进行验证,最后获得了该类复值神经网络的渐进周期解的存在性和唯一性.
The current research aims to investigate the existence of asymptotically almost periodic solu-tions in a particular class of complex-valued Hopfield neural networks with mixed time delays.Unlike most of the previous research efforts that primarily centered on real-valued neural networks, this paper takes into account the constraints of real-valued Hopfield neuralnetworks in addressing certain problems. It introduces a complex-valued network architecture to tackle complex-valued conditions that are insusceptible to direct processing within the real number domain.Notably, when the imaginary component of a complex-valued condition vanishes,the complex-valued system can seamlessly handle real numerical data. The investigation commences by dissecting the processing of complex data into its real and imaginary components for separate analysis.Employing the fixed-point theorem in Banach space, the exponential dichotomy property defined over the real number set, along with several differential equation inequality methods,the real and imaginary parts are rigorously examined.Ultimately, the research establishes the existence and uniqueness of asymptotically almost periodic solutions for the considered class of complex-valued neural networks.
关键词
参考文献 17
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