A competition model with herd behaviour and allee effect

Sen, Prosenjit; Maiti, Alakes; Samanta, G. P.

doi:10.2298/fil1908529s

Filomat

2019

DOI: 10.2298/fil1908529s

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A competition model with herd behaviour and allee effect

Prosenjit Sen

Alakes Maiti²,

G. P. Samanta

Abstract: In this work we have studied the deterministic behaviours of a competition model with herd behaviour and Allee effect. The uniform boundedness of the system has been studied. Criteria for local stability at equilibrium points are derived. The effect of discrete time-delay on the model is investigated. We have carried out numerical simulations to validate the analytical findings. The biological implications of our analytical and numerical findings are discussed.

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Cited by 2 publications

References 44 publications

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The influence of density in population dynamics with strong and weak Allee effect

Keya¹,

Kamrujjaman

Islam

2021

J Egypt Math Soc

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In this paper, we consider a reaction–diffusion model in population dynamics and study the impact of different types of Allee effects with logistic growth in the heterogeneous closed region. For strong Allee effects, usually, species unconditionally die out and an extinction-survival situation occurs when the effect is weak according to the resource and sparse functions. In particular, we study the impact of the multiplicative Allee effect in classical diffusion when the sparsity is either positive or negative. Negative sparsity implies a weak Allee effect, and the population survives in some domain and diverges otherwise. Positive sparsity gives a strong Allee effect, and the population extinct without any condition. The influence of Allee effects 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 diffusion 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.

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The influence of density in population dynamics with strong and weak Allee effect

Keya¹,

Kamrujjaman

Islam

2021

J Egypt Math Soc

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show abstract

The environmental effect on dynamics of the competition model with herd behavior

Stanković¹,

Jovanović²

2023

DCDS-B

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A competition model with herd behaviour and allee effect

Cited by 2 publications

References 44 publications

The influence of density in population dynamics with strong and weak Allee effect

The influence of density in population dynamics with strong and weak Allee effect

The environmental effect on dynamics of the competition model with herd behavior

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