拡散移動を伴う生物モデルの数学的考察

パッチネスと分岐理論

抄録

It has been observed that plankton displays spatial heterogeneity (patchiness) even though its environment appears homogeneous. As a model mechanism to explain this phenomenon, an interaction model is proposed which is in a prey-predator relationship. The model considered here is a generalized Lotka-Volterra system with diffusion. The results show that perturbations caused by fluctuations give rise to patchiness after long time: it depends on certain biological factors.
A mathematical tool is the theory of bifurcation for partial differential equations.