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Issue Math. Model. Nat. Phenom.
Volume 2, Number 4, 2007
Patterns and waves in ecology and evolution
Page(s) 105 - 121
DOI 10.1051/mmnp:2008027

Math. Model. Nat. Phenom. Vol. 2, No. 4, 2007, pp. 105-121
DOI: 10.1051/mmnp:2008027

Temporally Interruptive Interaction Allows Mutual Invasion of Two Competing Species Dispersing in Space

Hiromi Seno

Department of Mathematical and Life Sciences, Graduate School of Science, Hiroshima University, Kagamiyama 1-3-1, Higashi-hiroshima 739-8526, Japan

seno@math.sci.hiroshima-u.ac.jp

Abstract
With a reaction-diffusion system, we consider the dispersing two-species Lotka-Volterra model with a temporally periodic interruption of the interspecific competitive relationship. We assume that the competition coefficient becomes a given positive constant and zero by turns periodically in time. We investigate the condition for the coexistence of two competing species in space, especially in the bistable case for the population dynamics without dispersion. We could find that the spatial coexistence, that is, the spatially mutual invasion of two competing species appears with two opposite-directed travelling waves if a condition for the temporal interruption of the interspecific relationship is satisfied. Further, we give a suggested mathematical expression of the velocity of travelling waves.


Mathematics Subject Classification. 92D40, 92D25, 35Q80, 70K99, 92B05

Key words: population dynamics -- reaction-diffusion -- competition -- coexistence -- invasion -- Lotka-Volterra system




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