Rocha, J. LeonelTaha, A. K.Fournier-Prunaret, D.2019-03-122019-03-122016ROCHA, José Leonel; TAHA, A. K.; FOURNIER-PRUNARET, D. – Von Bertalanffy's dynamics under a polynomial correction: Allee effect and big bang bifurcation. In NOMA15 International Workshop on Nonlinear Maps and Applications (Journal of Physics: Conference Series). Dublin, Ireland: IOP Publishing, 2016. ISSN 1742-6588. Vol. 692/Pp. 1-111742-6588http://hdl.handle.net/10400.21/9707In 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.engvon Bertalanffy's functionsAllee effectconference object10.1088/1742-6596/692/1/012007