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Stability and periodic solutions of ordinary and functional differential equations
1 online resource (x, 337 pages) : illustrations
In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank.
Front Cover; Stability and Periodic Solutions of Ordinary and Functional Differential Equations; Copyright Page; Contents; Preface; Chapter 0 An Overview; 0.1 Survey of Chapter 1; 0.2 Survey of Chapter 2; 0.3 Survey of Chapter 3; 0.4 Survey of Chapter 4; Chapter 1 Linear Differential and Integrodifferential Equations; 1.0 The General Setting; 1.1 Linear Ordinary Differential Equations; 1.2 Periodic Solutions of Linear Differential Equations; 1.3 Linear Volterra Equations; 1.4 Periodic Solutions of Convolution Equations; 1.5 Periodic Solutions of Nonconvolution Equations.
1.6 Stability and BoundednessChapter 2 History, Motivation, Examples; 2.1 Classical Second-Order Equations; 2.2 Problems with a Delay; 2.3 Biology, Economics, and Epidemics; 2.4 Sources of Models; Chapter 3 Fixed-Point Theory; 3.1 Compactnes in Metric Spaces; 3.2 Contraction Mappings; 3.3 Existence Theorems for Linear Equations; 3.4 Schauder's Fixed-Point Theorem; 3.5 Existence Theorems for Nonlinear Equations; Chapter 4 Limit Sets, Periodicity, and Stability; 4.1 Ordinary Differential Equations; 4.2 Equations with Bounded Delays; 4.3 Volterra Equations with Infinite Delay.
4.4 Stability of Systems with Unbounded DelaysReferences; Author Index; Subject Index.
Includes bibliographical references (pages 325-331).
Équations différentielles fonctionnelles
Mathematics in science and engineering ; v. 178
1093215:10878051 Elsevier Science & Technology