Dynamical behaviors of a constant prey refuge ratio-dependent prey-predator model with Allee and fear effects  

作　　者：Soumitra Pal Pijush Panday Nikhil Pal A.K.Misra Joydev Chattopadhyays 

机构地区：[1]Department of Mathematics Institute of Science,Banaras Hindu University Varanasi 221005,India [2]Department of Mathematical and Statistical Sciences University of Alberta,Edmonton,AB T6G 2G1,Canada [3]Department of Mathematics,Visva-Bharati Santiniketan 731235,India [4]Agricultural and Ecological Research Unit Indian Statistical Institute 203,B.T.Road,Kolkata 700108,India

出　　处：《International Journal of Biomathematics》2024年第1期227-250,共24页生物数学学报（英文版）

基　　金：Soumitra Pal is thankful to the Council of Scientific and Industrial Research(CSIR),Government of India for providing financial support in the form of senior research fellowship(File No.09/013(0915)/2019-EMR-I).

摘　　要：In this paper,we consider a nonlinear ratio-dependent prey-predator model with constant prey refuge in the prey population.Both Allee and fear phenomena are incorporated explicitly in the growth rate of the prey population.The qualitative behaviors of the proposed model are investigated around the equilibrium points in detail.Hopf bifurcation including its direction and stability for the model is also studied.We observe that fear of predation risk can have both stabilizing and destabilizing effects and induces bubbling phenomenon in the system.It is also observed that for a fixed strength of fear,an increase in the Allee parameter makes the system unstable,whereas an increase in prey refuge drives the system toward stability.However,higher values of both the Allee and prey refuge parameters have negative impacts and the populations go to extinction.Further,we explore the variation of densities of the populations in different bi-parameter spaces,where the coexistence equilibrium point remains stable.Numerical simulations are carried out to explore the dynamical behaviors of the system with the help of MATLAB software.

关 键 词：Predator-prey system Allee effect fear effect prey refuge BIFURCATION population density 

分 类 号：O17[理学—数学]