Stability analysis of a stage‐structure model with spatial heterogeneity. (29th April 2021)

• Record Type: Journal Article
• Authors: Yan, Shuling; Guo, Shangjiang
• Is Part Of: Mathematical methods in the applied sciences. Volume 44:Number 14(2021)
• Page Start: 10993
• Page End: 11005
• Publication Date: 2021-04-29
• Subjects: Lotka‐Volterra competition -- spatial heterogeneity -- stability -- stage structure; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.7464
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : 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.