scholarly journals Global existence of solutions and uniform persistence of a diffusive predator–prey model with prey-taxis

2016 ◽  
Vol 260 (7) ◽  
pp. 5847-5874 ◽  
Author(s):  
Sainan Wu ◽  
Junping Shi ◽  
Boying Wu
Keyword(s):  
Global Existence ◽  
Existence Of Solutions ◽  
Uniform Persistence ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Global Existence Of Solutions ◽  
Prey Model

Global Solutions of a Diffusive Predator-Prey Model with Holling IV Functional Response

2013 ◽  
Vol 336-338 ◽  
pp. 664-667
Author(s):  
Yu Juan Jiao
Keyword(s):  
Functional Response ◽  
Existence Of Solutions ◽  
Uniform Boundedness ◽  
Global Solutions ◽  
Energy Estimates ◽  
Predator Prey ◽  
Cross Diffusion ◽  
Predator Prey Model ◽  
Global Existence Of Solutions ◽  
Prey Model

Using the energy estimates and Gagliardo-Nirenberg type inequalities, the uniform boundedness and global existence of solutions for a predator-prey model with Holling IV functional response with self- and cross-diffusion are proved.

Global attractivity of positive periodic solution for a predator–prey model with modified Leslie–Gower Holling-type II schemes and a deviating argument

2014 ◽  
Vol 07 (06) ◽  
pp. 1450071 ◽  
Author(s):  
Kai Wang ◽  
Yanling Zhu
Keyword(s):  
Lyapunov Functional ◽  
Global Attractivity ◽  
Sufficient Conditions ◽  
Positive Periodic Solution ◽  
Uniform Persistence ◽  
Type Ii ◽  
Predator Prey ◽  
Deviating Argument ◽  
Predator Prey Model ◽  
Prey Model

In this paper, by utilizing the comparison theorem and constructing a suitable Lyapunov functional the predator–prey model with modified Leslie–Gower Holling-type II schemes and a deviating argument is studied. Some sufficient conditions are obtained for uniform persistence and global attractivity of positive periodic solutions for this model. Furthermore, an example shows that the obtained criteria are easily verifiable.

scholarly journals Global existence and boundedness of solutions in a Lotka-Volterra reaction-diffusion system of predator-prey model with nonlinear prey-taxis

Filomat ◽  
2019 ◽  
Vol 33 (15) ◽  
pp. 5023-5035
Author(s):  
Demou Luo
Keyword(s):  
Global Existence ◽  
Boundary Conditions ◽  
Neumann Boundary ◽  
Reaction Diffusion ◽  
Classical Solutions ◽  
Boundedness Of Solutions ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Global Classical Solutions ◽  
Prey Model

In this paper, we investigate a diffusive Lotka-Volterra predator-prey model with nonlinear prey-taxis under Neumann boundary conditions. This system describes a prey-taxis mechanism that is an immediate movement of the predator u in response to a change of the prey v (which lead to the collection of u). We apply some methods to overcome the substantial difficulty of the existence of nonlinear prey-taxis term and prove that the unique global classical solutions of Lotka-Volterra predator-prey model are globally bounded.

scholarly journals Global existence of solutions to parabolic two species predator-prey chemotaxis system

2021 ◽  
Author(s):  
Arumugam Gurusamy ◽  
Gnanasekaran Shanmugasundaram ◽  
Nithyadevi nagarajan ◽  
Yang He
Keyword(s):  
Global Existence ◽  
Existence Of Solutions ◽  
Predator Prey ◽  
Global Existence Of Solutions ◽  
Chemotaxis System

Hopf bifurcation analysis of predator–prey model with two delays and disease transmission

2020 ◽  
Vol 13 (07) ◽  
pp. 2050068
Author(s):  
Renxiang Shi
Keyword(s):  
Periodic Solution ◽  
Hopf Bifurcation ◽  
Global Existence ◽  
Bifurcation Analysis ◽  
Disease Transmission ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey System ◽  
Prey Model ◽  
Two Delays

In this paper, we study the Hopf bifurcation of predator–prey system with two delays and disease transmission. Furthermore, the global existence of bifurcated periodic solution was studied, the influence of disease transmission is given. At last, some simulations are given to support our result.

scholarly journals Analysis on a Stochastic Predator-Prey Model with Modified Leslie-Gower Response

2011 ◽  
Vol 2011 ◽  
pp. 1-16 ◽  
Author(s):  
Jingliang Lv ◽  
Ke Wang
Keyword(s):  
Global Existence ◽  
Stochastic Model ◽  
Unique Solution ◽  
Stochastic System ◽  
Finite Time ◽  
Asymptotic Properties ◽  
Sufficient Conditions ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model

This paper presents an investigation of asymptotic properties of a stochastic predator-prey model with modified Leslie-Gower response. We obtain the global existence of positive unique solution of the stochastic model. That is, the solution of the system is positive and not to explode to infinity in a finite time. And we show some asymptotic properties of the stochastic system. Moreover, the sufficient conditions for persistence in mean and extinction are obtained. Finally we work out some figures to illustrate our main results.

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