Department of Mathematics, Bharathiar University, Coimbatore, 641 046 Tamilnadu India.
Department of Mathematics, and Research Center for Complex Systems and Network Sciences, Southeast University, Nanjing, 210096 Jiangsu China ; Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, 21589 Saudi Arabia.
Cogn Neurodyn. 2015 Apr;9(2):145-77. doi: 10.1007/s11571-014-9312-2. Epub 2014 Oct 9.
In this paper, the problem of the existence, uniqueness and uniform stability of memristor-based fractional-order neural networks (MFNNs) with two different types of memductance functions is extensively investigated. Moreover, we formulate the complex-valued memristor-based fractional-order neural networks (CVMFNNs) with two different types of memductance functions and analyze the existence, uniqueness and uniform stability of such networks. By using Banach contraction principle and analysis technique, some sufficient conditions are obtained to ensure the existence, uniqueness and uniform stability of the considered MFNNs and CVMFNNs with two different types of memductance functions. The analysis results establish from the theory of fractional-order differential equations with discontinuous right-hand sides. Finally, four numerical examples are presented to show the effectiveness of our theoretical results.
本文广泛研究了具有两种不同电感器函数的基于忆阻器的分数阶神经网络 (MFNN) 的存在性、唯一性和一致稳定性问题。此外，我们还构建了具有两种不同电感器函数的复值忆阻分数阶神经网络 (CVMFNN)，并分析了此类网络的存在性、唯一性和一致稳定性。通过使用巴拿赫压缩原理和分析技术，得到了一些充分条件，以确保具有两种不同电感器函数的所考虑的 MFNN 和 CVMFNN 的存在性、唯一性和一致稳定性。分析结果是从具有不连续右半部分的分数阶微分方程理论中得出的。最后，给出了四个数值实例，以验证我们理论结果的有效性。
