Long-time behavior of a class of diffusive predator–prey systems with fear cost and protection zone

2021 ◽  
pp. 107388
Author(s):  
Yaying Dong ◽  
Shanbing Li
Keyword(s):  
Time Behavior ◽  
Long Time Behavior ◽  
Predator Prey ◽  
Protection Zone ◽  
Long Time

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.

QUALITATIVE ANALYSIS OF A STOCHASTIC PREDATOR–PREY SYSTEM WITH DISEASE IN THE PREDATOR

2013 ◽  
Vol 06 (01) ◽  
pp. 1250068 ◽  
Author(s):  
SHUANG LI ◽  
XINAN ZHANG
Keyword(s):  
White Noise ◽  
Predator Population ◽  
Deterministic System ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Predator Prey ◽  
Prey System ◽  
Long Time ◽  
Global Positive Solution ◽  
Disease Free

A stochastic predator–prey system with disease in the predator population is proposed, the existence of global positive solution is derived. When the white noise is small, there is a stationary distribution. In addition, conditions of global stability for the deterministic system are also established from the above result. By Lyapunov function, the long time behavior of solution around the disease-free equilibrium of deterministic system is derived. These results mean that stochastic system has the similar property with the corresponding deterministic system. When the white noise is small, however, large environmental noise makes the result different. Finally, numerical simulations are carried out to support our findings.

Long-time behavior of a stochastic predator–prey model with modified Leslie–Gower and Holling-type II schemes

2016 ◽  
Vol 09 (03) ◽  
pp. 1650039 ◽  
Author(s):  
Yuguo Lin ◽  
Daqing Jiang
Keyword(s):  
Time Behavior ◽  
Type Ii ◽  
Invariant Density ◽  
Long Time Behavior ◽  
Singular Measure ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Long Time

In this paper, we consider a stochastic predator–prey model with modified Leslie–Gower and Holling-type II schemes. We analyze long-time behavior of densities of the distributions of the solution. We prove that the densities can converge in [Formula: see text] to an invariant density or can converge weakly to a singular measure under appropriate conditions.

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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