关键词: Dirichlet边界, 竞争模型, 分歧解, 稳定性

Abstract: The existence and stability of positive steady state solutions for a competition model with diffusion are studied under Dirichlet boundary condition. By using bifurcation theory and standard elliptic equations regularity theory, the existence of bifurcation solutions for steady state is analyzed. The sufficient condition of the existence is obtained and is verified by the numerical simulations. By the linear stability theory, the stable condition of bifurcation solutions is given. The research results show that the system can reach the stable coexistence state when the parameters satisfy certain conditions.

Key words: Dirichlet boundary, competition model, bifurcation solution, stability