Big Bang Bifurcation Analysis and Allee Effect in Generic Growth Functions - LAAS - Laboratoire d'Analyse et d'Architecture des Systèmes Accéder directement au contenu
Article Dans Une Revue International journal of bifurcation and chaos in applied sciences and engineering Année : 2016

Big Bang Bifurcation Analysis and Allee Effect in Generic Growth Functions

Résumé

The main purpose of this work is to study the dynamics and bifurcation properties of generic growth functions, which are defined by the population size functions of the generic growth equation. This family of unimodal maps naturally incorporates a principal focus of ecological and biological research: the Allee effect. The analysis of this kind of extinction phenomenon allows to identify a class of Allee’s functions and characterize the corresponding Allee’s effect region and Allee’s bifurcation curve. The bifurcation analysis is founded on the performance of fold and flip bifurcations. The dynamical behavior is rich with abundant complex bifurcation structures, the big bang bifurcations of the so-called “box-within-a-box” fractal type being the most outstanding. Moreover, these bifurcation cascades converge to different big bang bifurcation curves with distinct kinds of boxes, where for the corresponding parameter values several attractors are associated. To the best of our knowledge, these results represent an original contribution to clarify the big bang bifurcation analysis of continuous 1D maps.
Fichier non déposé

Dates et versions

hal-01760758 , version 1 (06-04-2018)

Identifiants

Citer

J. Leonel Rocha, Abdel-Kaddous Taha, D. Fournier-Prunaret. Big Bang Bifurcation Analysis and Allee Effect in Generic Growth Functions. International journal of bifurcation and chaos in applied sciences and engineering , 2016, 26 (06), ⟨10.1142/S021812741650108X⟩. ⟨hal-01760758⟩
34 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More