具有分布偏差变元的脉冲双曲型系统的振动性研究  

Study on Oscillation of Solutions for High-order Impulsive Hyperbolic System with Distributed Deviating Arguments

作　　者：朱先阳 吴迪[2,3] ZHU Xianyang;WU Di(School of Data Science,Tongren University,Tongren 554300,China;College of Electrical and Information Engineering,Hunan Institute of Engineering,Xiangtan 411104,China;National Engineering Research Center of RVC,Hunan University,Changsha 410082,China)

机构地区：[1]铜仁学院大数据学院,铜仁554300 [2]湖南工程学院电气与信息工程学院,湘潭411104 [3]湖南大学机器人视觉感知与控制技术国家工程研究中心,长沙410082

出　　处：《湖南工程学院学报(自然科学版)》2024年第4期57-64,共8页Journal of Hunan Institute of Engineering(Natural Science Edition)

基　　金：国家自然科学基金资助项目(11161024);铜仁学院博士科研启动基金项目(trxyDH2220);铜仁市科技计划项目(铜市科研〔2023〕42号).

摘　　要：脉冲时滞微分方程描述系统在不同时间点上受到不同力的作用,包括来自历史状态(时滞项)和突发事件(脉冲激励)的影响,这种系统与现实较接近,在多个领域有着广泛的应用.通过研究脉冲时滞微分方程,可以更好地预测和控制系统在脉冲变化下的行为,从而让系统在生物学、生态学、控制理论等多个领域中发挥重要作用.本文利用微分不等式和特征值方法,分别在Robin和Dirichlet边值条件下,得到了具有分布偏差变元的高阶脉冲时滞双曲型系统解振动性判定的两个充分条件.Impulsive delay differential equation describes a system that is subject to different forces at different points in time,including historical states(time-delay terms)and sudden events(impulsive excitation).It has a wide range of applications.By studying the system,we can better predict and control the behavior of the system under the change of pulse,which plays an important role in many fields such as biology,ecology,control theory and so on.In this paper,two sufficient conditions of oscillation of solutions for high-order impulsive hyperbolic systems with distributed deviating arguments are obtained by using differential inequalities and eigenvalue methods under Robin and Dirichlet boundary conditions respectively.

关 键 词：分布偏差变元 脉冲 反证法 充分条件 振动性 

分 类 号：O193[理学—数学]