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The minimal speed of traveling fronts for a diffusive Lotka-Volterra competition model (1998)

Hosono, Yuzo

Springer

Bulletin of mathematical biology 60 (1998), S. 435-448

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ISSN: 1522-9602

Source: Springer Online Journal Archives 1860-2000

Topics: Biology , Mathematics

Notes: Abstract 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.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1006/bulm.1997.0008

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Stability analysis of the phytoplankton vertical steady states in a laboratory test tube (1994)

Beretta, Edoardo ; Fasano, Antonio ; Hosono, Yuzo ; [et al.]

Chichester, West Sussex : Wiley-Blackwell

Mathematical Methods in the Applied Sciences 17 (1994), S. 551-575

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ISSN: 0170-4214

Keywords: Mathematics and Statistics ; Applied Mathematics

Source: Wiley InterScience Backfile Collection 1832-2000

Topics: Mathematics

Notes: The positive vertical equilibrium profiles of a phytoplankton population growing in a vertical test tube under controlled experimental conditions (temperature, salinity, light intensity at the top surface) for nutrients are discussed with reference to their stability properties for arbitrary positive initial values of the biomass concentration along the tube. Two different approaches are followed. First a stability result is established in the Sobolev norm H2 by estimating the norms of the perturbations recursively in successive subintervals of suitably small amplitude. The second approach provides stability in the sense of the uniform convergence as a corollary of a stability theorem for a rather general class of integro-differential equations.