Stability analysis of a stage-structure model with spatial heterogeneity

A stage-structure competition-diffusion model with spatial heterogeneity is investigated in this paper. Under some suitable assumptions, the existence of spatially non-homogeneous steady-state solutions is established by investigating eigenvalue problems with indefinite weight and employing Lyapunov-Schmidt reduction. The stability of spatially nonhomogeneous steady-state solutions is obtained by analyzing the set of the spectrum of the associated infinitesimal generator. In particular, the global stability of the steady-state solutions is described in weak competition case.

Automated summary

This paper investigates a stage-structure competition-diffusion model with spatial heterogeneity, establishing the existence and stability of spatially non-homogeneous steady-state solutions under suitable assumptions. The global stability of the steady-state solutions is particularly described in the case of weak competition.