Titre :	Non algebraic limit cycles for somes planar differential systems
Type de document :	texte imprimé
Auteurs :	Khaoula Khaouni, Auteur ; Rachid Cheurfa, Directeur de thèse
Editeur :	Sétif:UFS
Année de publication :	2024
Importance :	1 vol (52 f.)
Format :	29 cm
Langues :	Anglais (eng)
Catégories :	Thèses & Mémoires:Mathématique
Mots-clés :	Differential systems Equilibrium points The phase portrait Isolated periodic solutions non-algebraic Non-algebraic limit cycles
Index. décimale :	510-Mathématique
Résumé :	The objective of this work is the qualitative study of some classes of planar polynomial differential systems. The results obtained in this study concern the nature of equilibrium points, the phase portrait and the existence and no existence of no algebraic isolated periodic solutions consequently no algebraic limits cycles. Moreover we give an explicity expression of a limit cycle for two classes of differential cubic and quantic systems.
Note de contenu :	Sommaire Introduction3 1 DynamicalSystems5 1.1Introduction..................................5 1.2Polynomialdi¤erentailsystems.......................5 1.3VectorÂ…eld..................................6 1.4Phaseportrait.................................7 1.5Equilibriumpoint...............................8 1.6Stabilityoftheequilibriumpoints......................8 1.7Lineardynamicalsystem...........................8 1.8ClassiÂ…cationofequilibriumpointsofasystemintheplane(tr,det)...21 1.9Nonlineardynamicalsystems........................23 1.10Invariantcurve................................24 1.11Firstintegral.................................25 1.12Integratingfactors..............................25 1.13InverseIntegratingFactor..........................26 2 ItnroductiontothetheoryofLimitcycles28 2.1Introduction..................................28 2.2Notionoflimitcycles.............................29 2.3Stabilityoflimitcycles............................29 2.4Existencecriteriaforalgebraiclimitcycles.................30 2.5Existencecriteriaforperiodicsolutions...................32 2.6ThePoincaréreturnmap...........................34 3 Non-algebraiclimitcyclesforcubicsystems37 3.1Introduction..................................37 3.1.1Cubicsystems.............................38 3.1.2Theexplicitequationofthelimitcycle...............38 3.1.3Theuniquenessofthelimitcycle..................42 3.2Generalisation : Integrabilityandlimitcyclesformoregeneralclassesof cubicsystems.................................43 3.2.1Exampleofapplication........................48
Côte titre :	MAM/0712

Non algebraic limit cycles for somes planar differential systems [texte imprimé] / Khaoula Khaouni, Auteur ; Rachid Cheurfa, Directeur de thèse . - [S.l.] : Sétif:UFS, 2024 . - 1 vol (52 f.) ; 29 cm.
Langues : Anglais (eng)

Catégories :	Thèses & Mémoires:Mathématique
Mots-clés :	Differential systems Equilibrium points The phase portrait Isolated periodic solutions non-algebraic Non-algebraic limit cycles
Index. décimale :	510-Mathématique
Résumé :	The objective of this work is the qualitative study of some classes of planar polynomial differential systems. The results obtained in this study concern the nature of equilibrium points, the phase portrait and the existence and no existence of no algebraic isolated periodic solutions consequently no algebraic limits cycles. Moreover we give an explicity expression of a limit cycle for two classes of differential cubic and quantic systems.
Note de contenu :	Sommaire Introduction3 1 DynamicalSystems5 1.1Introduction..................................5 1.2Polynomialdi¤erentailsystems.......................5 1.3VectorÂ…eld..................................6 1.4Phaseportrait.................................7 1.5Equilibriumpoint...............................8 1.6Stabilityoftheequilibriumpoints......................8 1.7Lineardynamicalsystem...........................8 1.8ClassiÂ…cationofequilibriumpointsofasystemintheplane(tr,det)...21 1.9Nonlineardynamicalsystems........................23 1.10Invariantcurve................................24 1.11Firstintegral.................................25 1.12Integratingfactors..............................25 1.13InverseIntegratingFactor..........................26 2 ItnroductiontothetheoryofLimitcycles28 2.1Introduction..................................28 2.2Notionoflimitcycles.............................29 2.3Stabilityoflimitcycles............................29 2.4Existencecriteriaforalgebraiclimitcycles.................30 2.5Existencecriteriaforperiodicsolutions...................32 2.6ThePoincaréreturnmap...........................34 3 Non-algebraiclimitcyclesforcubicsystems37 3.1Introduction..................................37 3.1.1Cubicsystems.............................38 3.1.2Theexplicitequationofthelimitcycle...............38 3.1.3Theuniquenessofthelimitcycle..................42 3.2Generalisation : Integrabilityandlimitcyclesformoregeneralclassesof cubicsystems.................................43 3.2.1Exampleofapplication........................48
Côte titre :	MAM/0712