Traveling wave solutions for two species competitive chemotaxis systems

Issa, Tahir Bachar; Salako, Richadi B.; Shen, Wenxian

doi:10.1016/j.na.2021.112480

Cited by 6 publications

(4 citation statements)

References 34 publications

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“…Proof. It can be proved by the similar arguments as those of [12,Lemm 2.2]. For completeness, we provide a proof in the following.…”

Section: Stability Results On Fixed Unbounded Domainsmentioning

confidence: 59%

Vanishing-spreading dichotomy in a two-species chemotaxis competition system with a free boundary

Bao,

Shen

2021

Preprint

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Predicting the evolution of expanding population is critical to control biological threats such as invasive species and virus explosion. In this paper, we consider a two species chemotaxis system of parabolic-parabolic-elliptic type with Lotka-Volterra type competition terms and a free boundary. Such a model with a free boundary describes the spreading of new or invasive species subject to the influence of some chemical substances in an environment with a free boundary representing the spreading front. We first find conditions on the parameters which guarantee the global existence and boundedness of classical solutions with nonnegative initial functions. Next, we investigate vanishing-spreading dichotomy scenarios for positive solutions. It is shown that the vanishing-spreading dichotomy in the generalized sense always occurs; that the vanishing spreading dichotomy in the strong sense occurs when the competition between two species is weak-weak competition; and that the vanishing spreading dichotomy in the weak sense occurs when the competition between two species is weak-strong competition.

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“…Proof. It can be proved by the similar arguments as those of [12,Lemm 2.2]. For completeness, we provide a proof in the following.…”

Section: Stability Results On Fixed Unbounded Domainsmentioning

confidence: 59%

Vanishing-spreading dichotomy in a two-species chemotaxis competition system with a free boundary

Bao,

Shen

2021

Preprint

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“…In 1970, Keller and Segel proposed a celebrated mathematical model to describe the chemotaxis phenomenon [20,21]. Since these interesting works of Keller and Segel, many variants of chemotaxis models have been proposed and their dynamics have been studied intensively mainly on homogeneous environments [1,3,4,5,6,7,10,12,13,17,18,19,22,30,36,40] and [24,25,26,27,28,29,34,35,36,37,38,39]. In particular, we refer to the survey papers [2,8,9].…”

Section: Introduction and The Statements Of The Main Resultsmentioning

confidence: 99%

Pointwise persistence in full chemotaxis models with logistic source on bounded heterogeneous environments

Issa

Shen

2020

Journal of Mathematical Analysis and Applications

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“…Heuristically, this can be understood as the more sensitive species experiences stronger repulsion and keeps receding (thus becomes invaded by the other species), forming a traveling wave. We remark that when the system (1.6)-(1.7) only has one chemical that is emitted by both u and v, existence of traveling wave was recently established by [32].…”

Section: 2mentioning

confidence: 90%

Two-species competition model with chemotaxis: well-posedness, stability and dynamics

Li,

Yao

2021

Preprint

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We study a system of PDEs modeling the population dynamics of two competitive species whose spatial movements are governed by both diffusion and mutually repulsive chemotaxis effects. We prove that solutions to this system are globally well-posed, without any smallness assumptions on the chemotactic coefficients. Moreover, in the weak competition regime, we prove that neither species can be driven to extinction as the time goes to infinity, regardless of how strong the chemotaxis coefficients are. Finally, long-time behaviors of the system are studied both analytically in the weakly nonlinear regime, and numerically in the fully nonlinear regime.

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Traveling wave solutions for two species competitive chemotaxis systems

Cited by 6 publications

References 34 publications

Vanishing-spreading dichotomy in a two-species chemotaxis competition system with a free boundary

Vanishing-spreading dichotomy in a two-species chemotaxis competition system with a free boundary

Pointwise persistence in full chemotaxis models with logistic source on bounded heterogeneous environments

Two-species competition model with chemotaxis: well-posedness, stability and dynamics

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