Stability Analysis of Gompertz's Logistic Growth Equation Under Strong, Weak and No Allee Effects

摘要

The interest and the relevance of the study of population dynamics and extinction phenomenon are the main motivation to investigate the induction of Allee effects in Gompertz's logistic growth equation. The stability analysis of the equilibrium points of Gompertz's logistic growth equation under strong, weak and no Allee effects is presented. Properties and sufficient conditions for the existence of strong, weak and no Allee effects for these new continuous population growth models are provided and discussed. It is established a sufficient condition to prove that the time evolution of the population density to the stable equilibria gets larger, as the Allee effects get stronger. These continuous population growth models subjected to Allee effects take longer time to reach its equilibrium states. The developed models are validated using the Icelandic herring population, with GPDD Id. 1765.