| 基于忆阻的分数阶时滞复值神经网络的全局渐近稳定性 |
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| 引用本文： | 王利敏,宋乾坤,赵振江.基于忆阻的分数阶时滞复值神经网络的全局渐近稳定性[J].应用数学和力学,2017,38(3):333-346. |
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| 作者姓名： | 王利敏 宋乾坤 赵振江 |
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| 作者单位： | 1重庆交通大学 信息科学与工程学院, 重庆 400074;2重庆交通大学 数学系, 重庆 400074;3湖州师范学院 数学系, 浙江 湖州 313000 |
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| 基金项目： | 国家自然科学基金(61273021;61473332)，重庆市研究生科研创新项目(CYS16179)The National Natural Science Foundation of China(61273021 |
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| 摘 要： | 研究了分数阶复值神经网络的稳定性.针对一类基于忆阻的分数阶时滞复值神经网络,利用Caputo分数阶微分意义上Filippov解的概念, 研究其平衡点的存在性和唯一性.采用了将复值神经网络分离成实部和虚部的研究方法, 将实数域上的比较原理、不动点定理应用到稳定性分析中, 得到了模型平衡点存在性、唯一性和全局渐近稳定性的充分判据.数值仿真实例验证了获得结果的有效性.
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| 关 键 词： | 复值神经网络 分数阶微积分 忆阻器 Filippov解 全局渐近稳定性 |
| 收稿时间： | 2016-07-19 |
Global Asymptotic Stability of Memristor-Based Fractional-Order Complex-Valued Neural Networks With Time Delays |
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| WANG Li-min,SONG Qian-kun,ZHAO Zhen-jiang.Global Asymptotic Stability of Memristor-Based Fractional-Order Complex-Valued Neural Networks With Time Delays[J].Applied Mathematics and Mechanics,2017,38(3):333-346. |
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| Authors: | WANG Li-min SONG Qian-kun ZHAO Zhen-jiang |
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| Affiliation: | 1School of Information Science and Engineering, Chongqing Jiaotong University, Chongqing 400074, P.R.China;2Department of Mathematics, Chongqing Jiaotong University, Chongqing 400074, P.R.China;3Department of Mathematics, Huzhou Teachers University, Huzhou, Zhejiang 313000, P.R.China |
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| Abstract: | The global stability of fractional-order complex-valued neural networks was investigated.For a class of memristor-based fractional-order complex-valued neural networks with time delays,under the concept of the Filippov solution in the sense of Caputo's fractional derivation,the existence and uniqueness of the equilibrium point were discussed.The comparison principle and the fixed-point theorem were applied to the stability analysis through division of the complex values into the real part and the imaginary part.Some sufficient criteria for the global asymptotic stability of memristor-based fractional-order complex-valued neural networks were derived.Finally,a simulation example shows the effectiveness of the obtained results. |
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| Keywords: | complex-valued neural network fractional calculus memristor Filippov solution global asymptotic stability |
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