Keya et al. J Egypt Math Soc (2021) 29:4 https://doi.org/10.1186/s42787-021-00114-x Journal of the Egyptian Mathematical Society ORIGINAL RESEARCH Open Access The infuence of density in population dynamics with strong and weak Allee efect Kamrun Nahar Keya1, Md. Kamrujjaman2* and Md. Shafqul Islam3 *Correspondence:
[email protected] Abstract 2 Department In this paper, we consider a reaction–difusion model in population dynamics and of Mathematics, University of Dhaka, Dhaka 1000, study the impact of diferent types of Allee efects with logistic growth in the hetero- Bangladesh geneous closed region. For strong Allee efects, usually, species unconditionally die out Full list of author information and an extinction-survival situation occurs when the efect is weak according to the is available at the end of the article resource and sparse functions. In particular, we study the impact of the multiplicative Allee efect in classical difusion when the sparsity is either positive or negative. Nega- tive sparsity implies a weak Allee efect, and the population survives in some domain and diverges otherwise. Positive sparsity gives a strong Allee efect, and the popula- tion extinct without any condition. The infuence of Allee efects on the existence and persistence of positive steady states as well as global bifurcation diagrams is presented. The method of sub-super solutions is used for analyzing equations. The stability condi- tions and the region of positive solutions (multiple solutions may exist) are presented. When the difusion is absent, we consider the model with and without harvesting, which are initial value problems (IVPs) and study the local stability analysis and present bifurcation analysis.