| Titre : | Stability Analysis of Delay Di§erential Equation |
| Auteurs : | Wafa Ziza, Auteur ; Baya Laadjal, Directeur de thèse |
| Editeur : | Biskra [Algérie] : Faculté des Sciences Exactes et des Sciences de la Nature et de la Vie, Université Mohamed Khider, 2024 |
| Format : | 1 vol. (42 p.) / couv. ill. en coul / 30cm |
| Langues: | Anglais |
| Mots-clés: | delay differential equations, historic function , method of steps, existence and uniqueness of solutions, stability theory |
| Résumé : |
The study of delay differential equations (DDEs) aims to understand the behavior of systems where the current state depends not only on present conditions but also on past states. The main objective of this work is to discuss the existence and uniqueness of solutions and give an analytic method to solve DDEs. Furthermore, we aim to study the stability of both linear and nonlinear equations to determine the conditions under which the system remains stable. The analysis will include examining equilibrium points and characteristic equations. |
| Sommaire : |
Acknowledgements ii Abstract iii Contents iv List of figures vi Introduction 1 1 General results on delay di§erential equations 3 1.1 Existence and uniqueness of an initial value problem (IVP) of a DDE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.2 Solutions of delay di§erential equations . . . . . . . . . . . . . 7 1.2.1 Principle of method of steps: . . . . . . . . . . . . . . . . 7 1.2.2 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.3 Di§erence between ODEs and DDEs . . . . . . . . . . . . . . . 12 2 Stabilty of delay di§erential equations 15 2.1 Stability of equilibrium points . . . . . . . . . . . . . . . . . . . 16 2.2 A linear system of delay di§erential equations . . . . . . . . . 17 2.2.1 Characteristic equation of linear delay di§erential equation . . . . . . . .18 2.2.2 Stability of the linear delay di§erential equation . . . . 20 2.3 Local stability of nonlinear system of delay di§erential equations . . . 22 2.3.1 Linearization of nonlinear DDE . . . .. . . . . . . 22 2.3.2 Delay e§ects on stability . . . . . . . . . . . . . . 26 2.3.3 Applications on the stability . . . . . . . . . . 27 Conclusion 36 Bibliographie 36 Annexe A: Matlab codes for chapter 1 39 Annexe B: Abreviations and Notations 42 |
Disponibilité (1)
| Cote | Support | Localisation | Statut |
|---|---|---|---|
| MM/1289M1380 | Mémoire master | bibliothèque sciences exactes | Consultable |
