scholarly journals A diffusive one-prey and two-competing-predator system with a ratio-dependent functional response: I, long time behavior and stability of equilibria

2013 ◽  
Vol 397 (1) ◽  
pp. 9-28 ◽  
Author(s):  
Wonlyul Ko ◽  
Inkyung Ahn
Keyword(s):  
Functional Response ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Stability Of Equilibria ◽  
Long Time ◽  
Ratio Dependent ◽  
Predator System

Dynamic Analysis of a Stochastic Predator–Prey Model With Crowley–Martin Functional Response, Disease in Predator, and Saturation Incidence

2020 ◽  
Vol 15 (7) ◽  
Author(s):  
Conghui Xu ◽  
Yongguang Yu ◽  
Guojian Ren
Keyword(s):  
Functional Response ◽  
Existence And Uniqueness ◽  
Global Attractivity ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Disease In Predator ◽  
Long Time

Abstract This work aims to study some dynamical properties of a stochastic predator–prey model, which is considered under the combination of Crowley–Martin functional response, disease in predator, and saturation incidence. First, we discuss the existence and uniqueness of positive solution of the concerned stochastic model. Second, we prove that the solution is stochastically ultimate bounded. Then, we investigate the extinction and the long-time behavior of the solution. Furthermore, we establish some conditions for the global attractivity of the model. Finally, we propose some numerical simulations to illustrate our main results.

scholarly journals On global dynamics of 2D convective Cahn–Hilliard equation

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Xiaopeng Zhao
Keyword(s):  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Global Dynamics ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Initial Value ◽  
Hilliard Equation ◽  
Long Time ◽  
Cahn Hilliard Equation ◽  
Initial Boundary Value

AbstractIn this paper, we study the long time behavior of solution for the initial-boundary value problem of convective Cahn–Hilliard equation in a 2D case. We show that the equation has a global attractor in $H^{4}(\Omega )$ H 4 ( Ω ) when the initial value belongs to $H^{1}(\Omega )$ H 1 ( Ω ) .

The coupled Cahn–Hilliard/Allen–Cahn system with dynamic boundary conditions

2021 ◽  
pp. 1-27
Author(s):  
Ahmad Makki ◽  
Alain Miranville ◽  
Madalina Petcu
Keyword(s):  
Fractal Dimension ◽  
Boundary Conditions ◽  
Well Posedness ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Dynamic Boundary Conditions ◽  
Finite Dimensional ◽  
Dynamic Boundary ◽  
Long Time ◽  
Finite Fractal Dimension

In this article, we are interested in the study of the well-posedness as well as of the long time behavior, in terms of finite-dimensional attractors, of a coupled Allen–Cahn/Cahn–Hilliard system associated with dynamic boundary conditions. In particular, we prove the existence of the global attractor with finite fractal dimension.

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