| 研究実績の概要 |
With growing deterioration of the global environment, research on species diversity is gaining importance also from a theoretical point of view. We are interested in the study of a 3-species competition-diffusion (CD) system, in which coexistence of two otherwise incompatible species can occur thanks to the mediating influence of a third competitor (competitor-mediated coexistence). Such coexistence can be attained with complex spatio-temporal patterns in which two different traveling waves interact with each other. By studying the bifurcation structure of such waves in 1D, it is possible to understand the origin of and the transitions between such patterns. In particular, they are linked to the destabilization of a travelling pulse by Hopf bifurcation which leads first to a breathing (time-periodic) wave and then to wave reflection. In 2D this corresponds to the destabilization of regular spirals into breathing spirals and then their breakup into complex patterns.
Ideally, one would want to prove analytically under which conditions on the parameters coexistence occurs in the CD system. We started from discussing which situations cannot result in coexistence, thus limiting the parameter space inside which interesting phenomena may be observed. Extending our previous singular limit results, we have shown that coexistence is not possible when the growth rate of one species is very large (but still finite) or very small (but still positive).
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