The infuence of density in population dynamics with strong and weak Allee efect | ||||
Journal of the Egyptian Mathematical Society | ||||
Volume 29, Issue 1, 2021, Page 1-26 PDF (3.53 MB) | ||||
Document Type: Original Article | ||||
DOI: 10.1186/s42787-021-00114-x | ||||
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Authors | ||||
Kamrun Nahar Keya1; Md. Kamrujjaman* 2; Md. Shafqul Islam3 | ||||
1Department of Science and Humanities, Military Institue of Science and Technology, Dhaka 1216, Bangladesh. | ||||
2Department of Mathematics, University of Dhaka, Dhaka 1000, Bangladesh. | ||||
3School of Mathematical and Computational Sciences, University of Prince Edward Island, Charlottetown, PE, Canada. | ||||
Abstract | ||||
In this paper, we consider a reaction–difusion model in population dynamics and study the impact of diferent types of Allee efects with logistic growth in the heterogeneous closed region. For strong Allee efects, usually, species unconditionally die out and an extinction-survival situation occurs when the efect is weak according to the 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. Negative 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 population 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 conditions 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. We present a number of numerical examples to verify analytical results. | ||||
Keywords | ||||
Strong and weak Allee efect; Regular difusion; Global analysis; Bifurcation analysis; Extinction; Survival | ||||
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