具有时滞的扩散BAM神经网络的指数稳定性Global exponential stability in BAM networks with delays and reaction-diffusion terms
蔡玲霞;秦伶俐;胡洪晓;王凯;
摘要(Abstract):
研究一类具有反应扩散的滞后BAM神经网络平衡点的存在性唯一性和全局指数稳定性.运用拓扑同胚映射,Lyapunov泛函以及多参数方法,得到关于平衡点存在唯一性和全局指数稳定性的充分条件,将相关文献的结果推广到正整数r范数上.
关键词(KeyWords): BAM神经网络;Neumann边界条件;全局指数稳定性
基金项目(Foundation): 国家自然科学基金(11201399);; 新疆自治区高校科研计划(XJEDU2012S20)
作者(Authors): 蔡玲霞;秦伶俐;胡洪晓;王凯;
参考文献(References):
- [1]Bart Kosko.Adaptive bi-directional associative memories[J].Applied Optics,1987,26(23):4947-4960.
- [2]Bart Kosko.Bi-directional associative memories[J].IEEE Transaction on Systems,Man and Cybernetis,1988,18(1):49-60.
- [3]Song Qiankun,Cao Jinde.Global exponential stability and existence of periodic solutions in BAM networkswith delays and reaction-diffusion terms[J].Chaos,Solitons and Fractals,2005,23:421-430.
- [4]Cui Baotong,Lou Xuyang.Global asymptotic stability of BAM neural networks with distributed delays and reaction-diffusion terms[J].Chaos,Solitons and Fractals,2006,27:1347-1354.
- [5]Lou Xuyang,Cui Baotong,Wu Wei.On global exponential stability and existence of periodic solutions forBAM neural networks with distributed delays and reaction-diffusion terms[J].Chaos,Solitons and Fractals,2008,36:1044-1054.
- [6]陈宁.具有吸引项的反应扩散型和拟抛物方程解的全局死核问题[J].纯粹数学与应用数学,2004,20(3):248-254.
- [7]许丹丹,李艳玲,吴迪.一类带扩散项的HIV模型的平衡解的稳定性分析[J].纯粹数学与应用数学,2011,27(3):369-376.
- [8]李金花,惠小健,祁新雷.非线性反应扩散方程的广义条件对称及其精确解[J].纯粹数学与应用数学,2009,25(1):87-92.
- [9]Ju Hyun Park.A novel criterion for global asymptotic stability of BAM neural networks with time delays[J].Chaos,Solitons and Fractals,2006,29:446-453.