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Competitive exclusion and persistence in models of resource and sexual competition (1997)

Feng, Wei

Springer

Journal of mathematical biology 35 (1997), S. 683-694

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ISSN: 1432-1416

Keywords: Key words: Resource and sexual competition ; Population dynamics ; Reaction-diffusion systems ; Persistence and exclusion

Source: Springer Online Journal Archives 1860-2000

Topics: Biology , Mathematics

Notes: Abstract. We study a combined mathematical model of resource and sexual competition. The population dynamics in this model is analyzed through a coupled system of reaction-diffusion equations. It is shown that strong sexual competition and low birth rate lead to competitive exclusion of the biological species. If sexual competition is weak, then the persistence of the species is possible, depending on the initial density functions and the growth rates of the species. When sexual competition affects both species, persistence and competitive exclusion results are also obtained in terms of the ecological data in the model.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/s002850050071

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Stability and asymptotic behaviour in a reaction-diffusion system (1994)

Feng, Wei

Chichester, West Sussex : Wiley-Blackwell

Mathematical Methods in the Applied Sciences 17 (1994), S. 155-169

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ISSN: 0170-4214

Keywords: Mathematics and Statistics ; Applied Mathematics

Source: Wiley InterScience Backfile Collection 1832-2000

Topics: Mathematics

Notes: This paper is concerned with some qualitative analysis for a coupled system of five reaction-diffusion equations which arises from a physiology model. The uniform boundedness of the time-dependent solution is obtained under various boundary conditions. Sufficient conditions are also given to ensure the asymptotic stability of the non-negative steady-state solutions under Dirichlet or Robin boundary condition for each component. Under homogeneous Neumann boundary condition for some components the time-dependent solution is proven to converge to a constant steady state determined by the initial functions.