University Sétif 1 FERHAT ABBAS Faculty of Sciences
Détail de l'auteur
Auteur Khaoula Khaouni |
Documents disponibles écrits par cet auteur
Ajouter le résultat dans votre panier Affiner la recherche
Titre : Non algebraic limit cycles for somes planar differential systems Type de document : document électronique 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 cyclesIndex. 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........................48Côte titre : MAM/0712 En ligne : http://dspace.univ-setif.dz:8888/jspui/bitstream/123456789/5417/1/mam0712.pdf Non algebraic limit cycles for somes planar differential systems [document électronique] / 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 cyclesIndex. 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........................48Côte titre : MAM/0712 En ligne : http://dspace.univ-setif.dz:8888/jspui/bitstream/123456789/5417/1/mam0712.pdf Exemplaires (1)
Code-barres Cote Support Localisation Section Disponibilité MAM/0712 MAM/0712 Livre Bibliothèque des sciences Anglais Disponible
Disponible
