Existence of wave front solutions and estimates of wave speed for a competition-diffusion system

Kanel, Jacob; Zhou, Li

doi:10.1016/0362-546x(95)00221-g

Cited by 49 publications

(23 citation statements)

References 5 publications

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“…A partial result was obtained by Hosono (1995), on which the present result relies. We also refer to papers by Kanel and Zhou (1996) and Tang and Fife (1980), which showed the existence of traveling waves for equation (1.1) and gave the estimates of the minimal wave speed, respectively, but both of them dealt with situations different from ours. In the following sections, we focus attention on the minimal speed of traveling waves under assumption (1.3).…”

Section: By Solving This For the Heaviside Initial Condition And By Ementioning

confidence: 99%

The Minimal Speed of Traveling Fronts for a Diffusive Lotka–Volterra Competition Model

Hosono

1998

Bulletin of Mathematical Biology

145

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This paper concerns the minimal speed of traveling wave fronts for a two-species diffusion-competition model of the Lotka-Volterra type. An earlier paper used this model to discuss the speed of invasion of the gray squirrel by estimating the model parameters from field data, and predicted its speed by the use of a heuristic analytical argument. We discuss the conditions which assure the validity of their argument and show numerically the existence of the realistic range of parameter values for which their heuristic argument does not hold. Especially for the case of the strong interaction of two competing species compared with the intraspecific competition, we show that all parameters appearing in the system affect the minimal speed of invasion.

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Section: By Solving This For the Heaviside Initial Condition And By Ementioning

confidence: 99%

The Minimal Speed of Traveling Fronts for a Diffusive Lotka–Volterra Competition Model

Hosono

1998

Bulletin of Mathematical Biology

145

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“…Kanel and Zhou [16] further proved that (1.5) has travelling front solutions connecting the equilibria E 1 and E * . Conley and Gardner [5] and Gardner [8] showed that (1.5) has travelling front solutions connecting the equilibria E 1 and E 2 , where Conley index and degree theory methods have been developed.…”

Section: Introductionmentioning

confidence: 96%

Existence of travelling wave solutions in delayed reaction–diffusion systems with applications to diffusion–competition systems

2006

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This paper is concerned with the existence of travelling wave solutions in a class of delayed reaction-diffusion systems without monotonicity, which concludes two-species diffusion-competition models with delays. Previous methods do not apply in solving these problems because the reaction terms do not satisfy either the so-called quasimonotonicity condition or non-quasimonotonicity condition. By using Schauder's fixed point theorem, a new cross-iteration scheme is given to establish the existence of travelling wave solutions. More precisely, by using such a new cross-iteration, we reduce the existence of travelling wave solutions to the existence of an admissible pair of upper and lower solutions which are easy to construct in practice. To illustrate our main results, we study the existence of travelling wave solutions in two delayed two-species diffusion-competition systems.Mathematics Subject Classification: 35K57, 35R20, 92D25

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“…Taking random movement of the species into account, a model to describe the competition among two distinct species is the following Lotka-Volterra competition-diffusion system (1.2) where u 1 ( x , t ), u 2 ( x , t ) stand for the population densities of two competing species, respectively, and all the parameters are positive. Existence of traveling waves connecting the different equilibria was widely investigated by kinds of methods, see [4,7,[9][10][11][12][13][14]17,30] and some references cited therein. It is well known that time delays seem to be inevitable accounting for a variety of causes, such as the period of hatching, duration of gestation, the maturation time of the species.…”

Section: Introductionmentioning

confidence: 99%

Traveling waves for n-species competitive system with nonlocal dispersals and delays

Xia¹,

Dong³

et al. 2016

Applied Mathematics and Computation

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Existence of wave front solutions and estimates of wave speed for a competition-diffusion system

Cited by 49 publications

References 5 publications

The Minimal Speed of Traveling Fronts for a Diffusive Lotka–Volterra Competition Model

The Minimal Speed of Traveling Fronts for a Diffusive Lotka–Volterra Competition Model

Existence of travelling wave solutions in delayed reaction–diffusion systems with applications to diffusion–competition systems

Traveling waves for n-species competitive system with nonlocal dispersals and delays

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