A-2-2 Theta logisticモデル付きFisher-Kolmogorov方程式と分岐現象(生物モデル)

抄録

This paper shows the pitchfork bifurcation arising in the Fisher-Kolmogorov(F-K) equation with the theta logistic model in the context of the dynamical systems. Studies of the F-K equation have mainly focused on the travelling waves so far. In the original paper of Fisher, p(the frequency of the mutant gene) and q(the frequency of its parent allelomorph) are presented by such a differential equation as a diffusion equation with the logistic model. We consider the theta logistic model on the F-K equation. Using the multi-scale analysis, the pitchfork bifurcation occurs when the sign of the growth rate of the theta logistic mode changes from minus to plus.