Dynamical analysis of a Lotka-Volterra competition model with both Allee and fear effects  

作　　者：Shangming Chen Fengde Chen Vaibhava Srivastava Rana D.Parshad 

机构地区：[1]School of Mathematics and Statistics,Fuzhou University Fuzhou,Fujian 350108,P.R.China [2]Department of Mathematics,Iowa State University Ames,IA50011,USA

出　　处：《International Journal of Biomathematics》2024年第8期175-222,共48页生物数学学报(英文版)

摘　　要：Population ecology theory is replete with density-dependent processes.However,traitmediated or behavioral indirect interactions can both reinforce or oppose densitydependent effects.This paper presents the first two species competitive ODE and PDE systems,where the non-consumptive behavioral fear effect and the Allee effect,a densitydependent process,are both present.The stability of the equilibria is discussed analytically using the qualitative theory of ordinary differential equations.It is found that the Allee effect and the fear effect change the extinction dynamics of the system and the number of positive equilibrium points,but they do not affect the stability of the positive equilibria.We also observe standard co-dimension one bifurcation in the system by varying the Allee or fear parameter.Interestingly,we find that the Allee effect working in conjunction with the fear effect can bring about several dynamical changes to the system with only fear.There are three parametric regimes of interest in the fear parameter.For small and intermediate amounts of fear,the Allee+fear effect opposes dynamics driven by the fear effect.However,for large amounts of fear the Allee+fear effect reinforces the dynamics driven by the fear effect.The analysis of the corresponding spatially explicit model is also presented.To this end,the comparison principle for parabolic PDE is used.The conclusions of this paper have strong implications for conservation biology,biological control as well as the preservation of biodiversity.

关 键 词：Competition model Allee effect fear effect stability BIFURCATION reactiondiffusion system 

分 类 号：O175[理学—数学]