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

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International Journal of Biomathematics 2024年第1期17卷 227-250页

作者： Soumitra Pal Pijush Panday Nikhil Pal A.K.Misra Joydev Chattopadhyays Department of Mathematics Institute of Science Banaras Hindu University Varanasi 221005India Department of Mathematical and Statistical Sciences University of Alberta EdmontonAB T6G 2G1Canada Department of Mathematics Visva-Bharati Santiniketan 731235India Agricultural and Ecological Research Unit Indian Statistical Institute 203 B.T.RoadKolkata 700108India

In this paper,we consider a nonlinear ratio-dependent prey-predator model with constant prey refuge in the prey *** Allee and fear phenomena are incorporated explicitly in the growth rate of the prey *** qualitative behaviors of the proposed model are investigated around the equilibrium points in *** bifurcation including its direction and stability for the model is also *** observe that fear of predation risk can have both stabilizing and destabilizing effects and induces bubbling phenomenon in the *** 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 ***,higher values of both the Allee and prey refuge parameters have negative impacts and the populations go to ***,we explore the variation of densities of the populations in different bi-parameter spaces,where the coexistence equilibrium point remains *** 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

Switching effect on a two prey-one predator system with strong Allee effect incorporating prey refuge

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International Journal of Biomathematics 2024年第2期17卷 1-50页

作者： Sangeeta Saha Guruprasad Samanta Department of Mathematics Indian Institute of Engineering Science and Technology Shibpur Howrah 711103India

In an environment,the food chains are balanced by the prey-predator *** a predator species is provided with more than one prey population,it avails the option of prey switching between prey species according to their ***,prey switching of predators mainly helps to increase the overall growth rate of a predator *** this work,we have proposed a two prey-one predator system where the predator population adopts switching behavior between two prey species at the time of *** the prey population exhibit a strong Allee effect and the predator population is considered to be a generalist *** proposed system is biologically well-defined as the system variables are positive and do not increase abruptly with *** local stability analysis reveals that all the predator-free equilibria are saddle points whereas the prey-free equilibrium is always *** intrinsic growth rates of prey,the strong Allee parameters,and the prey refuge parameters are chosen to be the controlling parameters *** numerical simulation reveals that in absence of one prey,the other prey refuge parameter can change the system dynamics by forming a stable or unstable limit ***,a situation of bi-stability,tri-stability,or even multi-stability of equilibrium points occurs in this *** in presence of the switching effect,the predator chooses prey according to their abundance,so,increasing refuge in one prey population decreases the count of the second prey *** is also observed that the count of predator population reaches a comparatively higher value even if they get one prey population at its fullest quantity and only a portion of other prey ***,in the scarcity of one prey species,switching to the other prey is beneficial for the growth of the predator population.

关键词： prey-predator model switching effect strong Allee effect prey refuge

Existence of spatiotemporal patterns in the reaction-diffusion predator-prey model incorporating prey refuge

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International Journal of Biomathematics 2016年第6期9卷 87-111页

作者： Lakshmi Narayan Guin Benukar Mondal Santabrata Chakravarty Department of Mathematics Visva-BharatiSantiniketan-731 235 West Bengal India

The pattern formation in reaction-diffusion system has long been the subject of interest to the researchers in the domain of mathematical ecology because of its universal exis- tence and importance. The present investigation deals with a spatial dynamics of the Beddington-DeAngelis predator-prey model in the presence of a constant proportion of prey refuge. The model system representing boundary value problem under study is subjected to homogeneous Neumann boundary conditions. The asymptotic stability including the local and the global stability and the bifurcation as well of the unique pos- itive homogeneous steady state of the corresponding temporal model has been analyzed. The Turing instability region in two-parameter space and the condition of diffusion- driven instability of the spatiotemporal model are investigated. Based on the appro- priate numerical simulations, the present model dynamics in Turing space appears to get influenced by prey refuge while it exhibits diffusion-controlled pattern formation growth to spots, stripe-spot mixtures, labyrinthine, stripe-hole mixtures and holes repli- cation. The results obtained appear to enrich the findings of the model system under consideration.

关键词： Beddington DeAngelis functional response prey refuge stability reaction-diffusion predator-prey model spatiotemporal pattern.

NONCONSTANT prey HARVESTING IN RATIO-DEPENDENT PREDATOR-prey SYSTEM INCORPORATING A CONSTANT prey refuge

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International Journal of Biomathematics 2012年第2期5卷 85-104页

作者： SAPNA DEVI DST Centre for Interdisciplinary Mathematical Sciences Banaras Hindu University Varanasi-221005 India

This paper deals with the problem of nonconstant harvesting of prey in a ratio-dependent predator-prey system incorporating a constant prey refuge. Here we use the reasonable catch-rate function instead of usual catch-per-unit-effort hypothesis. The existence, as well as the stability of possible equilibria, is carried out. Bionomic equilibrium of the system is determined and optimal harvest policy is studied with the help of Pontryagin＇s maximum principle. The key results developed in this paper are illustrated using numer- ical simulations. Our results indicate that dynamic behavior of the system very much depends on the prey refuge parameter and increasing amount of refuge could increase prey density and may lead to the extinction of predator population density.

关键词： Predator-prey prey refuge taxation ratio-dependent stability bionomic equilibrium harvesting optimal equilibrium.

A Leslie-Gower Holling Type-II Predator-prey Mathematical Model with Disease in prey Population Incorporating a prey refuge

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Journal of Mathematics and System Science 2016年第10期6卷 395-408页

作者： P. Mandal N. Das S. Pal Department of Mathematics Hooghly Mohsin College Chinsurah Hooghly India. Department of Mathematics Maulana Azad College Kolkata India. Department of Mathematics University of Kalyani Nadia lndia.

We formulate and analyze a predator-prey model followed by Leslie-Gower model in which the prey population is infected by disease. We assume that the disease can only spread over prey population. As a result prey population has been classified into two categories, namely susceptible prey, infected prey where as the predator population remains free from infection. To investigate the behaviour of prey population we incorporate prey refuge in this model. Since the prey refuge decreases the predation rate then it has an important effect in our predator-prey interaction model. We have discussed the existence of various equilibrium points and local stability analysis at those equilibrium points. We investigate the Hopf-bifurcation analysis about the interior equilibrium point by taking the rate of infection parameter and the prey refuge parameter as bifurcation parameters. The numerical analysis is carried out to support the analytical results and to discuss some interesting results that our model exhibits.

关键词： Predator and prey Disease transmission prey refuge Stability Hopf-bifurcation.

HOPF BIFURCATION OF AN INFECTED PREDATOR-prey SYSTEM WITH prey refuge

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Annals of Differential Equations 2013年第1期29卷 44-50页

作者： Yanwei Liu Xia Liu Dept. of Math. Zhoukou Normal University College of Math. and Information Science Henan Normal University

In this paper, an infected predator-prey model with prey refuge is investigated. The effects of refuge on the stability of the equilibria of the system are analyzed. Moreover, using the criterion introduced by Liu, we... 详细信息

关键词： infected prey Hopf bifurcation prey refuge stability

prey-predator model with functional response for optimal harvesting incorporating prey refuge

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International Journal of Biomathematics 2016年第1期9卷 265-285页

作者： G. S. Mahapatra P. Santra Department of MathematicsNational Institute of Technology Puducherry Karaikal 609605 India Department of MathematicsAbada New Set Up Upper Primary School Howrah West Bengal India

This paper presents a prey-predator model considering the predator interacting with non-refuges prey by class of functional responses. Here we also consider harvesting for only non-refuges prey. We discuss the equilibria of the model, and their stability for hiding prey either in constant form or proportional to the densities of prey population. We also investigate various possibilities of bionomic equilibrium and optimal harvesting policy. Finally we present numerical examples with pictorial presentation of the various effects of the prey predator system parameter.

关键词： prey-predator functional response prey refuge stability bionomic equilib-rium optimal harvesting.

GLOBAL DYNAMICS OF A PREDATOR-prey MODEL WITH prey refuge AND DISEASE

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Annals of Applied Mathematics 2018年第1期34卷 80-93页

作者： Zaowang Xiao Zhong Li College of Math.and Computer Science Fuzhou University

In this paper, we study a predator-prey model with prey refuge and disease. We study the local asymptotic stability of the equilibriums of the system. Further, we show that the equilibria are globally asymptotically stable if the equilibria are locaUy asymptotically stable. Some examples are presented to verify our main results. Finally, we give a brief discussion.

关键词： predator-prey model prey refuge disease stability

Global Stability Analysis and Optimal Taxation Control for a Harvested prey Predator System with prey refuge 26th

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Global Stability Analysis and Optimal Taxation Control for a...