| 摘要:（摘要内容经过系统自动伪原创处理以避免复制，下载原文正常，内容请直接查看目录。） 1892年，俄国力学家李雅普诺夫(Lyapunov)在他的论文《活动稳固性的普通成绩》中给出了活动稳固性的严厉数学界说和普通办法，俄语论文网站，从而奠基了稳固性实际的基本。跟着科技的提高，李雅普诺夫稳固性实际在许多范畴获得普遍运用和成长，俄语论文范文，重要表现在物文科学、工程技巧、生态体系、遗传成绩、神经收集等范畴。本文运用“类比法”结构李雅普诺夫函数研究二阶、三阶具有时滞的非线性微分体系的稳固性和有界性成绩。全文共分四部门。序文部门重要引见高阶微分方程的稳固性研究状态和本文任务的意义。第一章：根本界说和引理。第二章：研究一类二阶滞后型非线性微分体系的解的有界性成绩，本章成果推行了文[20]的成果，并处理了非齐次二阶滞后型非线性微分体系的有界性成绩。第三章：研究一类三阶滞后型非线性微分体系的全局渐近稳固性。本章成果推行了文[21一22]的成果。 Abstract: In 1892, Russian dynamicist Lyapunov (Lyapunov) in his doctoral thesis, the stability of the ordinary achievement "given in the activity stability of the strict mathematical definition and general way, thus laid a foundation for the stability of actual basic. Along with the improvement of science and technology, the Lyapunov stable practical in many fields obtained widespread application and development, it is important to performance in the field of the science, engineering technique, ecological system, genetic grades, neural network and so on. In this paper, the application of the analogy of structure Lyapunov function research of second order, third order with nonlinear delay differential system stability and boundedness results. Full text is divided into four departments. Preface to the introduction of the high order differential equations of the stability of the state and the significance of this task. The first chapter: the basic definition and lemma. The second chapter: Research for a class of second order lag of solutions of nonlinear differential system, boundedness results, this chapter results implementation of the results of paper [20], and dealt with the non homogeneous second order delay nonlinear differential system, boundedness results. In the third chapter, the global asymptotic stability of a class of three order nonlinear differential systems is studied. This chapter has carried out the results of the paper [21 and 22]. 目录: 序言 7-9 第一章 预备知识 9-10 第二章 对于二阶时滞微分方程的有界性 10-19 第三章 一类三阶时滞微分方程的全局渐近稳定性 19-26 参考文献 26-28 致谢 28 |
