时标上二阶拟线性延迟阻尼动态系统的动力学行为分析  

Dynamical Behavior of Second-order Quasilinear Delay Damped Dynamic Equations on Time Scales

作　　者：李继猛 杨甲山 LI JIMENG;YANG JIASHAN(School of Science,Shaoyang University,Shaoyang 422004,China;School of Data Science and Software Engineering,Wuzhou University,Wuzhou 543002,China)

机构地区：[1]邵阳学院理学院,邵阳422004 [2]梧州学院大数据与软件工程学院,梧州543002

出　　处：《应用数学学报》2020年第5期853-864,共12页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(51765060)项目;湖南省教育厅教学改革研究项目(HNJG-2020-0807)以及湖南省教育厅研究项目经费(19C1668)资助。

摘　　要：研究了时标T上一类二阶拟线性的变延迟阻尼动态系统的动力学行为,考虑的是系统为非正则情形(即∫t0∞[a-1(s)e-b/a(s,t0)]1/λ△s<∞的情形),通过引入广义Riccati变换,借助时标上的理论和一些经典不等式,建立了该系统振动的一些新准则,这些准则充分反应了延迟函数和阻尼项在系统振动中的影响作用.最后举例说明,所得准则不仅推广,改进并丰富了一些已知结果,而且具有较好的有效性和实用性.The dynamical behavior of certain second-order quasilinear variable delay damped dynamic equations are investigated on a time scale T,where the equations are noncanonical form(i.e.,∫t0∞[a-1(s)e-b/a(s,t0)]1/λ△s<∞).By using the generalized Riccati transformation,and in combination with the time scales theory and the classical inequality,some new oscillation criteria for the equation are established.The results fully reflect the influential actions of delay functions and damping terms in system oscillation.Finally,some examples are given to show that our results extend,improve and enrich those reported in the literature,and that they have good effectiveness and practicability.

关 键 词：动力学性质 时标 泛函动态系统 RICCATI变换 变延迟 

分 类 号：O175.7[理学—数学]