一类具多比例时滞脉冲递归神经网络的稳定性分析  

Stability analysis of a class of impulsive recurrent neural networks with multi-proportional delays

作　　者：宋协慧 周立群[1] SONG Xiehui;ZHOU Liqun(College of Mathematical Science,Tianjin Normal University,Tianjin 300387,China)

机构地区：[1]天津师范大学数学科学学院,天津300387

出　　处：《天津师范大学学报（自然科学版）》2020年第5期1-8,共8页Journal of Tianjin Normal University：Natural Science Edition

基　　金：天津市自然科学基金资助项目(18JCYBJC85800);天津市中青年骨干教师培养计划资助项目(135205GC38).

摘　　要：通过设计2个Lyapunov泛函和应用不等式技巧讨论了一类具多比例时滞的脉冲递归神经网络的稳定性,得到了保证该系统全局渐近稳定性和全局多项式稳定性的新的判定准则,并得到,就收敛速度而言,系统的渐近稳定性弱于多项式稳定性和指数稳定性.最后,通过数值算例及其仿真验证了结论的正确性和有效性.The stability of a class of impulsive recurrent neural networks with multi-proportional delays is discussed by designing two Lyapunov functionals and applying inequality skills.Several new criteria which guarantee global asymptotic stability and global polynomial stability of the system are obtained.It is obtained that both exponential stability and polynomial stability are stronger than asymptotic stability in terms of the convergence rate.Finally,a numerical example and its simulations are used to verify the correctness and effectiveness of the results.

关 键 词：比例时滞 脉冲效应 渐近稳定性 多项式稳定性 递归神经网络 LYAPUNOV泛函 

分 类 号：O175.13[理学—数学] TP183[理学—基础数学]