Titre :	On the predator–prey system with strong Allee effect in prey
Type de document :	texte imprimé
Auteurs :	Aya MELAAB, Auteur ; Nabil Beroual, Directeur de thèse
Editeur :	Sétif:UFA1
Année de publication :	2025
Importance :	1 vol (64 f.)
Format :	29 cm
Langues :	Anglais (eng)
Catégories :	Thèses & Mémoires:Mathématique
Mots-clés :	Predator–prey System strong Allee effect Bifurcation Limit cycles Coexistence Heteroclinic loop
Index. décimale :	510-Mathématique
Résumé :	Abstract In this thesis, we conduct a global bifurcation analysis of a general class of predator–prey models incorporating a strong Allee effect in the prey population. We highlight the existence of a heteroclinic loop connecting two saddle points and investigate the occurrence of Hopf bifurcation. Depending on parameter ranges, we also prove the existence, uniqueness, or nonexistence of a limit cycle. For a unique critical parameter value, a threshold curve separates regions of overexploitation (prey extinction) and coexistence (successful predator invasion) in the space of initial conditions. To illustrate our theoretical results, we provide several numerical examples. This work is primarily based on the article by Jinfeng Wang, Junping Shi, and Junjie Wei entitled *Predator–prey system with strong Allee effect in prey*.
Note de contenu :	Contents Introduction 3 1 Basicconceptsofecologyanddynamicalsystems 5 1.1 Basicconceptsofecology . .............................. 5 1.1.1 Glossary . .................................. 5 1.1.2 Interactionbetweenpopulations . ...................... 6 1.1.3 DefinitionoftheAlleeEffect . ........................ 7 1.2 Basicconceptsofmathematics . ........................... 8 1.2.1 SomeDefinitions . .............................. 8 1.2.2 ConceptofLimitCycle . ........................... 16 1.3 BasicConceptsintheEcologicalModel . ...................... 20 1.3.1 DynamicModelofaSinglePopulation . .................. 20 1.3.2 Two-SpeciesModels . ............................. 23 2 Onthepredator–preysystemwithstrongAlleeeffectinprey 31 2.1 Phaseplaneanalysis . ................................ 32 2.1.1 EquilibriumPoints . ............................. 33 2.2 StabilityAnalysis . .................................. 34 2.3 Hopfbifurcation . ................................... 42 2.4 Theuniquenessoflimitcycle . ........................... 45 3 Examplesanddiscussion 52 3.1 CubicModelwithHollingTypeIIFunctionalResponse . ............. 52 3.1.1 APrototypicalModel . ............................ 52 3.1.2 Equilibruimpoints . ............................. 53 3.1.3 HopfBifurcation . .............................. 53 3.1.4 UniquenessoftheLimitCycle . ....................... 53 3.1.5 NonexistenceofPeriodicOrbits . ...................... 54 3.2 CubicModelwithLinearFunctionalResponse . ................. 56 3.3 Boukal–Sabelis–Berecmodel . ............................ 58 Conclusion 61
Côte titre :	MAM/0768

On the predator–prey system with strong Allee effect in prey [texte imprimé] / Aya MELAAB, Auteur ; Nabil Beroual, Directeur de thèse . - [S.l.] : Sétif:UFA1, 2025 . - 1 vol (64 f.) ; 29 cm.
Langues : Anglais (eng)

Catégories :	Thèses & Mémoires:Mathématique
Mots-clés :	Predator–prey System strong Allee effect Bifurcation Limit cycles Coexistence Heteroclinic loop
Index. décimale :	510-Mathématique
Résumé :	Abstract In this thesis, we conduct a global bifurcation analysis of a general class of predator–prey models incorporating a strong Allee effect in the prey population. We highlight the existence of a heteroclinic loop connecting two saddle points and investigate the occurrence of Hopf bifurcation. Depending on parameter ranges, we also prove the existence, uniqueness, or nonexistence of a limit cycle. For a unique critical parameter value, a threshold curve separates regions of overexploitation (prey extinction) and coexistence (successful predator invasion) in the space of initial conditions. To illustrate our theoretical results, we provide several numerical examples. This work is primarily based on the article by Jinfeng Wang, Junping Shi, and Junjie Wei entitled *Predator–prey system with strong Allee effect in prey*.
Note de contenu :	Contents Introduction 3 1 Basicconceptsofecologyanddynamicalsystems 5 1.1 Basicconceptsofecology . .............................. 5 1.1.1 Glossary . .................................. 5 1.1.2 Interactionbetweenpopulations . ...................... 6 1.1.3 DefinitionoftheAlleeEffect . ........................ 7 1.2 Basicconceptsofmathematics . ........................... 8 1.2.1 SomeDefinitions . .............................. 8 1.2.2 ConceptofLimitCycle . ........................... 16 1.3 BasicConceptsintheEcologicalModel . ...................... 20 1.3.1 DynamicModelofaSinglePopulation . .................. 20 1.3.2 Two-SpeciesModels . ............................. 23 2 Onthepredator–preysystemwithstrongAlleeeffectinprey 31 2.1 Phaseplaneanalysis . ................................ 32 2.1.1 EquilibriumPoints . ............................. 33 2.2 StabilityAnalysis . .................................. 34 2.3 Hopfbifurcation . ................................... 42 2.4 Theuniquenessoflimitcycle . ........................... 45 3 Examplesanddiscussion 52 3.1 CubicModelwithHollingTypeIIFunctionalResponse . ............. 52 3.1.1 APrototypicalModel . ............................ 52 3.1.2 Equilibruimpoints . ............................. 53 3.1.3 HopfBifurcation . .............................. 53 3.1.4 UniquenessoftheLimitCycle . ....................... 53 3.1.5 NonexistenceofPeriodicOrbits . ...................... 54 3.2 CubicModelwithLinearFunctionalResponse . ................. 56 3.3 Boukal–Sabelis–Berecmodel . ............................ 58 Conclusion 61
Côte titre :	MAM/0768