Von Bertalanffy's dynamics under a polynomial correction: Allee effect and big bang bifurcation

International Workshop on Nonlinear Maps and Applications 2015

Rocha, J. Leonel^1 ; Taha, A.K.^2 ; Fournier-Prunaret, D.^3

ISEL-Instituto Superior de Engenharia de Lisboa, ADM, Rua Conselheiro Emídio Navarro 1, Lisboa

1959-007, Portugal^1

INSA, University of Toulouse, 135 Avenue du Rangueil, Toulouse

31077, France^2

LAAS-CNRS, INSA, University of Toulouse, 7 Avenue du Colonel Roche, Toulouse

31077, France^3

关键词: Asymptotic weight;    Bifurcation analysis;    Bifurcation structures;    Complex bifurcation;    Correction factors;    Discrete dynamical systems;    Dynamical approaches;    Growth equation;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/692/1/012007/pdf
DOI  :  10.1088/1742-6596/692/1/012007

来源: IOP

【 摘 要 】

In this work we consider new one-dimensional populational discrete dynamical systems in which the growth of the population is described by a family of von Bertalanffy's functions, as a dynamical approach to von Bertalanffy's growth equation. The purpose of introducing Allee effect in those models is satisfied under a correction factor of polynomial type. We study classes of von Bertalanffy's functions with different types of Allee effect: strong and weak Allee's functions. Dependent on the variation of four parameters, von Bertalanffy's functions also includes another class of important functions: functions with no Allee effect. The complex bifurcation structures of these von Bertalanffy's functions is investigated in detail. We verified that this family of functions has particular bifurcation structures: the big bang bifurcation of the so-called "box-within-a-box" type. The big bang bifurcation is associated to the asymptotic weight or carrying capacity. This work is a contribution to the study of the big bang bifurcation analysis for continuous maps and their relationship with explosion birth and extinction phenomena.