University Sétif 1 FERHAT ABBAS Faculty of Sciences
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Auteur Khaoula Khaouni |
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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 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 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 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 Exemplaires
Code-barres Cote Support Localisation Section Disponibilité aucun exemplaire
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 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 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 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 Exemplaires
Code-barres Cote Support Localisation Section Disponibilité aucun exemplaire
