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2013 Ecological systems, nonlinear boundary conditions, and $\Sigma$-shaped bifurcation curves
Kathryn Ashley, Victoria Sincavage, Jerome Goddard II
Involve 6(4): 399-430 (2013). DOI: 10.2140/involve.2013.6.399


We examine a one-dimensional reaction diffusion model with a weak Allee growth rate that appears in population dynamics. We combine grazing with a certain nonlinear boundary condition that models negative density dependent dispersal on the boundary and analyze the effects on the steady states. In particular, we study the bifurcation curve of positive steady states as the grazing parameter is varied. Our results are acquired through the adaptation of a quadrature method and Mathematica computations. Specifically, we computationally ascertain the existence of Σ-shaped bifurcation curves with several positive steady states for a certain range of the grazing parameter.


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Kathryn Ashley. Victoria Sincavage. Jerome Goddard II. "Ecological systems, nonlinear boundary conditions, and $\Sigma$-shaped bifurcation curves." Involve 6 (4) 399 - 430, 2013.


Received: 23 July 2012; Revised: 4 April 2013; Accepted: 10 April 2013; Published: 2013
First available in Project Euclid: 20 December 2017

zbMATH: 1281.34035
MathSciNet: MR3115975
Digital Object Identifier: 10.2140/involve.2013.6.399

Primary: 34B08 , 34B18

Keywords: Nonlinear boundary conditions , ‎positive‎ ‎solutions , weak Allee effect

Rights: Copyright © 2013 Mathematical Sciences Publishers


Vol.6 • No. 4 • 2013
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