A reaction-diffusion system of a competitor-competitor-mutualist model

Zheng, Sining

doi:10.1016/0022-247x(87)90038-2

Cited by 34 publications

(20 citation statements)

References 12 publications

(12 reference statements)

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“…The non-negative solutions of (I) are in fact the steady states (time-independent) of a parabolic system known as Competitor-Competitor-Mutualist model, see [12,15]. In this model, u 1 , u 2 and u 3 represent the population densities of two competitor and a mutualist, m and are the mutualist constants, and d i , i = 1, 2, 3 are the diffusion coefficients.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Positive Steady States of a Competitor-Competitor-Mutualist Model

Chen

Wang

2004

Acta Mathematicae Applicatae Sinica, English Series

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Section: Introduction and Main Resultsmentioning

confidence: 99%

Positive Steady States of a Competitor-Competitor-Mutualist Model

Chen

Wang

2004

Acta Mathematicae Applicatae Sinica, English Series

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“…Following the proof of Theorem 4.3 of Zheng (1986) [49] (see also Theorem 3.3 of Zheng (1987) [50]) one deduces that if S < 1 then E 0 = 0, the trivial equilibrium of (4)- (2)- (8) is globally asymptotically stable i.e., lim…”

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confidence: 89%

“…[50]) and by using the concept of upper/lower solution one proves that when l > l * cont. , system (4)- (2)- (8) …”

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confidence: 98%

FKPP equation with impulses on unbounded domain

Yatat

Dumont

2017

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This paper deals with the problem of travelling wave solutions in a scalar impulsive FKPP-like equation. It is a first step of a more general study that aims to address existence of travelling wave solutions for systems of impulsive reactiondiffusion equations that model ecological systems dynamics such as fire-prone savannas. Using results on scalar recursion equations, we show existence of populated vs. extinction travelling waves invasion and compute an explicit expression of their spreading speed (characterized as the minimal speed of such travelling waves). In particular, we find that the spreading speed explicitly depends on the time between two successive impulses. In addition, we carry out a comparison with the case of time-continuous events. We also show that depending on the time between two successive impulses, the spreading speed with pulse events could be lower, equal or greater than the spreading speed in the case of time-continuous events. Finally, we apply our results to a model of fire-prone grasslands and show that pulse fires event may slow down the grassland vs. bare soil invasion speed.

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“…The O. D. E. problem associated with (1.1)-(1.3) was proposed and studied by Rai et al in [11]. In [16] Zheng studied problem (1.1)-(1.3) as well as the Neumann problem in the case where all coefficients are constant. He proved the existence of semitrivial nonnegative equilibrium solutions and discussed the asymptotic stability of both such solutions and the trivial equilibrium solutions.…”

Section: Introductionmentioning

confidence: 97%