Persistence in reaction diffusion models with weak allee effect

Journal of Mathematical Biology
Junping Shi, Ratnasingham Shivaji

Abstract

We study the positive steady state distributions and dynamical behavior of reaction-diffusion equation with weak allele effect type growth, in which the growth rate per capita is not monotonic as in logistic type, and the habitat is assumed to be a heterogeneous bounded region. The existence of multiple steady states is shown, and the global bifurcation diagrams are obtained. Results are applied to a reaction-diffusion model with type II functional response, and also a model with density-dependent diffusion of animal aggregation.

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Citations

Mar 13, 2010·Journal of Mathematical Biology·Jinfeng WangJunjie Wei
Dec 11, 2008·Bulletin of Mathematical Biology·H BerestyckiP A Zegeling
Dec 15, 2015·The American Naturalist·Sharon BewickWilliam F Fagan
Mar 3, 2012·Journal of Theoretical Biology·Davide VergniMassimo Cencini
May 17, 2011·Mathematical Biosciences·Vicenç MéndezDaniel Campos
Jan 20, 2017·Journal of Mathematical Biology·Ying Zhou, William F Fagan

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