Stability and Oscillations in Delay Differential Equations of Population Dynamics
Stability and Oscillations in Delay Differential Equations of Population Dynamics
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DOI：
10.1007/978-94-015-7920-9
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发表时间：
1992-03
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影响因子：
--
通讯作者：
K. Gopalsamy
中科院分区：
文献类型：
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作者：
K. Gopalsamy
这本专著明确地概述了自治时滞微分方程稳定性和振动性的最新进展。主题包括线性和非线性时滞和积分微分方程，它们在生物和物理动态过程中都有潜在的应用。第一章分析了时滞Logistic方程的动力学特征，给出了一些与标量时滞方程和积分微分方程解的稳定性、振动性和比较有关的技巧和结果。第二章以教程的形式介绍了时滞诱导的周期Hopf分支的研究以及分析分支周期解的稳定性的相关计算。第三章讨论了非线性模型系统的局部分析，讨论了适用于线性方程及其摄动的多种方法。第四章讨论了非线性系统平衡态的全局收敛问题，并讨论了非线性系统关于平衡点的振动性。第三章和第四章对具有时滞的竞争和合作系统进行了定性分析。最后，第五章讨论了中立型微分方程组模型的最新发展及其在种群动力学中的应用。每一章最后都有一些练习，整个论述推荐这一卷作为研究生课程的很好的补充文本。适用于工作涉及泛函微分方程的数学家，他们的兴趣超出了线性稳定性分析的范围。
This monograph provides a definitive overview of recent advances in the stability and oscillation of autonomous delay differential equations. Topics include linear and nonlinear delay and integrodifferential equations, which have potential applications to both biological and physical dynamic processes. Chapter 1 deals with an analysis of the dynamical characteristics of the delay logistic equation, and a number of techniques and results relating to stability, oscillation and comparison of scalar delay and integrodifferential equations are presented. Chapter 2 provides a tutorial-style introduction to the study of delay-induced Hopf bifurcation to periodicity and the related computations for the analysis of the stability of bifurcating periodic solutions. Chapter 3 is devoted to local analyses of nonlinear model systems and discusses many methods applicable to linear equations and their perturbations. Chapter 4 considers global convergence to equilibrium states of nonlinear systems, and includes oscillations of nonlinear systems about their equilibria. Qualitative analyses of both competitive and cooperative systems with time delays feature in both Chapters 3 and 4. Finally, Chapter 5 deals with recent developments in models of neutral differential equations and their applications to population dynamics. Each chapter concludes with a number of exercises and the overall exposition recommends this volume as a good supplementary text for graduate courses. For mathematicians whose work involves functional differential equations, and whose interest extends beyond the boundaries of linear stability analysis.