We studied the nonlocal effects of intraspecific prey competition on the stability of the critical points of the Rosenzweig-MacArthur model and the Holling-Tanner model, respectively, using linear stability analysis. In particular we focused on the study of the stability of the coexistence state influenced by the nonlocality for both models. For each model, we used three different kernel functions to describe the nonlocal intraspecific prey competition. Based on our analysis, we found that the nonlocality plays a key role in affecting the stability of the coexistence point of both models with the given kernels. In addition, we conducted weakly nonlinear analysis of the coexistence state of the Holling-Tanner model with step kernel to confirm our stability results by linear stability analysis and explore the behavior in the neighborhood of the coexistence state.

Last modified

• 03/13/2018

Creator

• Jiang Zhuo

DOI

• https://doi.org/10.21985/N2P094

Subject

• Engineering Sciences and Applied Mathematics

Keyword

• Applied Mathematics

Date created

• 2017-01-01

Resource type

• Dissertation

Rights statement

• In Copyright