摘要
为了分析脉冲干扰因素对复数域神经网络的影响,研究了一类具有脉冲干扰的变时滞复数域CohenGrossberg神经网络的平衡点的动态行为.在假定放大函数、自反馈函数以及激活函数定义在复数域的情况下,首先,利用M矩阵和同胚映射的相关原理,分析了该系统平衡点的存在性和唯一性;其次,利用向量Lyapunov函数法以及数学归纳法,研究了该系统平衡点的全局模指数稳定性,并建立的稳定性判据;最后,通过两个数值仿真算例验证了所得结论的实用性和正确性.仿真结果显示系统状态在0.5 s便可收敛到平衡状态.研究结果表明:时滞和脉冲干扰强度越大、放大函数越小,则神经元状态的指数收敛速度越慢.
To analyse the effect of impulsive disturbances on neural networks,the dynamical behaviour of these disturbances was examined at the module of the equilibrium point of a class of complex-valued Cohen-Grossberg neural networks with time-varying delays.It was assumed that amplification,self-feedback,and activation functions were defined in a complex number domain.First,the existence and uniqueness of the equilibrium point of the system were analysed by utilising the corresponding property of the M matrix and the theorem of homeomorphism mapping.Second,the globally exponential stability of the module of the equilibrium point of the system was studied by applying the vector Lyapunov function and mathematical induction methods.The corresponding stability criteria were then established.Finally,two numerical examples from simulations were given to illustrate the practicability and correctness of the obtained results.The simulation results revealed that the states of the addressed system can reach equilibrium within 0.5 s.Other results showed that the greater the delay and impulsive strength and the smaller the amplification,the slower was the state convergence rate.
作者
徐晓惠
徐全
施继忠
张继业
陈子龙
XU Xiaohui;XU Quan;SHI Jizhong;ZHANG Jiye;CHEN Zilong(Key Laboratory of Automobile Measurement and Control&Safty,Xihua University,Chengdu 610039,China;Key Laboratory of Fluid and Power Machinery,Ministry of Education,Xihua University,Chengdu 610039,China;School of Technology,Xihua University,Chengdu 610039,China;College of Engineering,Zhejiang Normal University,Jinhua 321004,China;National Traction Power Laboratory,Southwest Jiaotong University,Chengdu 610031,China)
出处
《西南交通大学学报》
EI
CSCD
北大核心
2018年第4期820-828,共9页
Journal of Southwest Jiaotong University
基金
国家自然科学基金资助项目(11402214
11572264)
四川省教育厅自然科学重点项目(17ZA0364
16ZB0163)
四川省青年科技创新研究团队(2017TD0035
2017TD0026
2015TD0021
2016HH0010)
浙江省自然科学基金资助项目(LY14E08006)
作者简介
徐晓惠(1982—),女,副教授,研究方向为复杂非线性关联大系统的稳定性分析与控制,E-mail:xhxu@163.com。;通信作者:徐全(1982-),男,副教授,博士,研究方向为分数阶复杂关联系统的动态行为,E-mail:quanxnjd@sina.com。
