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Study of Fractional Order Tri-Tropic Prey-Predator Model with fear effect on Prey Population

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Advances in Pure Mathematics 2022年第11期12卷 652-675页

作者： Subrata Paul Animesh Mahata Supriya Mukherjee Prakash Chandra Mali Banamali Roy Department of Mathematics Arambagh Government Polytechnic Arambagh India Mahadevnagar High School Maheshtala Kolkata India Department of Mathematics Gurudas College Narkeldanga Kolkata India Department of Mathematics Jadavpur University Kolkata India Department of Mathematics Bangabasi Evening College Kolkata India

In this manuscript, we have studied a fractional-order tri-trophic model with the help of Caputo operator. The total population is divided into three parts, namely prey, intermediate predator and top predator. In addition, the predator fear impact on prey population is suggested in this paper. Existence and uniqueness along with non-negativity and boundedness of the model system have been investigated. We have studied the local stability at all equilibrium points. Also, we have discussed global stability and Hopf bifurcation of our suggested model at interior equilibrium point. The Adam-Bashforth-Moulton approach is utilized to approximate the solution to the proposed model. With the help of MATLAB, we were able to conduct graphical demonstrations and numerical simulations.

关键词： Prey-Predator Model Stability fear effect Hopf Bifurcation

Dynamical behavior of a delayed prey-predator-scavenger system with fear effect and linear harvesting

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International Journal of Biomathematics 2021年第4期14卷 159-188页

作者： Xin-You Meng Jie Li School of Science Lanzhou University of Technology LanzhouGansu 730050P.R.China College of Technology and Engineering Lanzhou University of Technology Lanzhou Gansu 730050P.R.China

In this paper,we propose a delayed prey-predator-scavenger system with fear effect and linear harvesting.First,we discuss the existence and stability of all possible equilibria.Next,we investigate the existence of Hopf bifurcation of the delayed system by regarding the gestation period of the scavenger as a bifurcation parameter.Furthermore,we obtain the direction of Hopf bifurcation and the stability of bifurcating periodic solutions by using the normal form theory and the central manifold theorem.In addition,we give the optimal harvesting strategy of the delayed system based on Pontryagin's maximum principle with delay.Finally,some numerical simulations are carried out to verify our theoretical results.

关键词： Prey-predator-scavenger fear effect time delay Hopf bifurcation optimal harvesting policy

The impact of fear effect on the dynamics of a delayed predator-prey model with stage structure

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生物数学学报:英文版 2023年第8期16卷 263-296页

作者： Qi Cao Guotai Chen Wensheng Yang School of Mathematics and Statistics Fujian Normal University Fuzhou 350117 FujianP.R.China FJKLMAA and Center for Applied Mathematics of Fujian Province(FJNU)Fuzhou350117 FujianP.R.China

In this paper,a stage structure predator-prey model consisting of three nonlinear ordinary differential equations is proposed and analyzed.The prey populations are divided into two parts:juvenile prey and adult prey.From extensive experimental data,it has been found that prey fear of predators can alter the physiological behavior of individual prey,and the fear effect reduces their reproductive rate and increases their mortality.In addition,we also consider the presence of constant ratio refuge in adult prey populations.Moreover,we consider the existence of intraspecific competition between adult prey species and predator species separately in our model and also introduce the gestation delay of predators to obtain a more realistic and natural eco-dynamic behaviors.We study the positivity and boundedness of the solution of the non-delayed system and analyze the existence of various equilibria and the stability of the system at these equilibria.Next by choosing the intra-specific competition coeficient of adult prey as bifurcation parameter,we demonstrate that Hopf bifurcation may occur near the positive equilibrium point.Then by taking the gestation delay as bifurcation parameter,the suficient conditions for the existence of Hopf bifurcation of the delayed system at the positive equilibrium point are given.And the direction of Hopf bifurcation and the stability of the periodic solution are analyzed by using the center manifold theorem and normal form theory.What's more,numerical experiments are performed to test the theoretical results obtained in this paper.

关键词： Stage-structure model fear effect time delay Hopf bifurcation

THE STABILITY OF A PREDATOR-PREY MODEL WITH fear effect IN PREY AND SQUARE ROOT FUNCTIONAL RESPONSE

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Annals of Applied Mathematics 2020年第2期36卷 186-194页

作者： Ying Huang Zhong Li College of Mathematics and Computer Science Fuzhou UniversityFuzhou 350108FujianPR China

In this paper, we consider a predator-prey model with fear effect and square root functional response. We give the singularity of the origin and discuss the stability and Hopf bifurcation of the trivial equilibrium and the positive equilibrium. We show that the fear effect has no effect on prey density, but will lead to the decrease of predator populations.

关键词： predator-prey fear effect stability Hopf bifurcation

Qualitative analysis of a diffusive predator–prey model with Allee and fear effects

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International Journal of Biomathematics 2021年第6期14卷 1-31页

作者： Jia Liu Jiangsu Vocational College of Electronics and Information Huaian 223003 P.R.China

In this study,we consider a diffusive predator-prey model with multiple Allee effects induced by fear factors.We investigate the existence,boundedness and permanence of the solution of the system.We also discuss the existence and non-existence of non-constant solutions.We derive sufficient conditions for spatially homogeneous(non-homogenous)Hopf bifurcation and steady state bifurcation.Theoretical and numerical simulations show that strong Allee effect and fear effect have great effect on the dynamics of system.

关键词： Predator-prey diffusion fear effect Allee effect bifurcation