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.

scholarly journals Global Behavior for a Strongly Coupled Predator-Prey Model with One Resource and Two Consumers

2012 ◽  
Vol 2012 ◽  
pp. 1-25
Author(s):  
Yujuan Jiao ◽  
Shengmao Fu
Keyword(s):  
Functional Response ◽  
Sufficient Conditions ◽  
Uniform Boundedness ◽  
Global Solutions ◽  
Energy Estimates ◽  
Positive Equilibrium ◽  
Strongly Coupled ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model

We consider a strongly coupled predator-prey model with one resource and two consumers, in which the first consumer species feeds on the resource according to the Holling II functional response, while the second consumer species feeds on the resource following the Beddington-DeAngelis functional response, and they compete for the common resource. Using the energy estimates and Gagliardo-Nirenberg-type inequalities, the existence and uniform boundedness of global solutions for the model are proved. Meanwhile, the sufficient conditions for global asymptotic stability of the positive equilibrium for this model are given by constructing a Lyapunov function.

scholarly journals Dynamical behavior of a stochastic predator-prey model with general functional response and nonlinear jump-diffusion

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Xinhong Zhang ◽  
Qing Yang
Keyword(s):  
Functional Response ◽  
Dynamical Behavior ◽  
Uniform Boundedness ◽  
Jump Diffusion ◽  
Necessary Condition ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
A New Technique ◽  
The One

<p style='text-indent:20px;'>In this paper, we consider a stochastic predator-prey model with general functional response, which is perturbed by nonlinear Lévy jumps. Firstly, We show that this model has a unique global positive solution with uniform boundedness of <inline-formula><tex-math id="M1">\begin{document}$ \theta\in(0,1] $\end{document}</tex-math></inline-formula>-th moment. Secondly, we obtain the threshold for extinction and exponential ergodicity of the one-dimensional Logistic system with nonlinear perturbations. Then based on the results of Logistic system, we introduce a new technique to study the ergodic stationary distribution for the stochastic predator-prey model with general functional response and nonlinear jump-diffusion, and derive the sufficient and almost necessary condition for extinction and ergodicity.</p>

EXISTENCE OF GLOBAL SOLUTIONS FOR A PREY–PREDATOR MODEL WITH CROSS-DIFFUSION

2010 ◽  
Vol 03 (02) ◽  
pp. 161-172 ◽  
Author(s):  
SHENGHU XU ◽  
WEIDONG LV
Keyword(s):  
Neumann Boundary Condition ◽  
Space Dimension ◽  
Existence Of Solutions ◽  
Global Solutions ◽  
Neumann Boundary ◽  
Energy Estimates ◽  
Cross Diffusion ◽  
Global Existence Of Solutions ◽  
Homogeneous Neumann Boundary Condition ◽  
Predator Model

In this paper, a ratio-dependent prey–predator model with cross-diffusion and homogeneous Neumann boundary condition is studied. Using the energy estimates and the bootstrap arguments, the global existence of solutions for the model is investigated when the space dimension is less than ten.

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