Global boundedness and asymptotic behavior in a two-species chemotaxis-competition system with two signals

2019 ◽  
Vol 48 ◽  
pp. 288-325 ◽  
Author(s):  
Guoqiang Ren ◽  
Bin Liu
Keyword(s):  
Asymptotic Behavior ◽  
Competition System ◽  
Global Boundedness

scholarly journals Dynamics of Gilpin-Ayala competition model with random perturbation

Filomat ◽  
2010 ◽  
Vol 24 (1) ◽  
pp. 101-113 ◽  
Author(s):  
Maja Vasilova ◽  
Miljana Jovanovic
Keyword(s):  
Asymptotic Behavior ◽  
Positive Solution ◽  
Finite Time ◽  
Random Perturbation ◽  
Competition Model ◽  
Competition System ◽  
Subject Classifications ◽  
Mathematics Subject Classifications

In this paper we study the Gilpin-Ayala competition system with random perturbation which is more general and more realistic than the classical Lotka-Volterra competition model. We verify that the positive solution of the system does not explode in a finite time. Furthermore, it is stochastically ultimately bounded and continuous a.s. We also obtain certain results about asymptotic behavior of the stochastic Gilpin-Ayala competition model. 2010 Mathematics Subject Classifications. 60H10, 34K50. .

Asymptotic Behavior of a Stochastic Two-Species Competition System with Impulsive Effects

2018 ◽  
Vol 19 (5) ◽  
pp. 427-438
Author(s):  
Pan Wang ◽  
Bing Li ◽  
Yongkun Li
Keyword(s):  
Asymptotic Behavior ◽  
Global Attractivity ◽  
Sufficient Conditions ◽  
Impulsive Effects ◽  
Species Competition ◽  
Stochastic Permanence ◽  
Competition System ◽  
Stochastic Boundedness ◽  
Dynamical Properties ◽  
Persistent In Mean

AbstractIn this paper, we consider a stochastic two-species competition system with impulsive effects. Some dynamical properties are investigated and sufficient conditions for the stochastic boundedness, stochastic permanence and global attractivity are established. Under some conditions, we conclude that the stochastic model is persistent in mean and extinction. An example is given to illustrate the main result.

Global boundedness and asymptotic behavior in a quasilinear attraction–repulsion chemotaxis model with nonlinear signal production and logistic-type source

2020 ◽  
Vol 30 (13) ◽  
pp. 2619-2689
Author(s):  
Guoqiang Ren ◽  
Bin Liu
Keyword(s):  
Asymptotic Behavior ◽  
Initial Data ◽  
Global Existence ◽  
Classical Solutions ◽  
Chemotaxis Model ◽  
Signal Production ◽  
Nonlinear Signal ◽  
Nonlinear Signal Production ◽  
Global Boundedness

In this work, we consider the quasilinear attraction–repulsion chemotaxis model with nonlinear signal production and logistic-type source. We present the global existence of classical solutions under appropriate regularity assumptions on the initial data. In addition, the asymptotic behavior of the solutions is studied, and our results generalize and improve some well-known results in the literature.

scholarly journals Boundedness and Asymptotic Behavior to a Chemotaxis System with Indirect Signal Generation and Singular Sensitivity

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Jie Wu ◽  
Li Zhao ◽  
Heping Pan
Keyword(s):  
Asymptotic Behavior ◽  
Boundary Conditions ◽  
Bounded Domain ◽  
Smooth Boundary ◽  
Rates Of Convergence ◽  
Signal Generation ◽  
Heat Semigroup ◽  
Singular Sensitivity ◽  
Chemotaxis System ◽  
Global Boundedness

In this paper, we consider the following indirect signal generation and singular sensitivity n t = Δ n + χ ∇ ⋅ n / φ c ∇ c ,   x ∈ Ω , t > 0 , c t = Δ c − c + w ,   x ∈ Ω , t > 0 , w t = Δ w − w + n ,   x ∈ Ω , t > 0 , in a bounded domain Ω ⊂ R N N = 2 , 3 with smooth boundary ∂ Ω . Under the nonflux boundary conditions for n , c , and w , we first eliminate the singularity of φ c by using the Neumann heat semigroup and then establish the global boundedness and rates of convergence for solution.

scholarly journals Analysis of Stochastic Gilpin-Ayala Competition System

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Lei Liu ◽  
Quanxin Zhu
Keyword(s):  
Asymptotic Behavior ◽  
Asymptotic Property ◽  
Stationary Distribution ◽  
Sufficient Conditions ◽  
Competition System

This paper is concerned with the asymptotic behavior for stochastic Gilpin-Ayala competition system. The sufficient conditions for existence of stationary distribution and extinction are established. And a certain asymptotic property of the solution is also obtained. A nontrivial example is provided to illustrate our results.

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