Electron. J. Diff. Equ., Vol. 2014 (2014), No. 88, pp. 1-27.

Halo-shaped bifurcation curves in ecological systems

Jerome Goddard II, Ratnasingham Shivaji

We examine the structure of positive steady state solutions for a diffusive population model with logistic growth and negative density dependent emigration on the boundary. In particular, this class of nonlinear boundary conditions depends on both the population density and the diffusion coefficient. Results in the one-dimensional case are established via quadrature methods. Additionally, we discuss the existence of a Halo-shaped bifurcation curve.

Submitted December 30, 2013. Published April 2, 2014.
Math Subject Classifications: 34B18, 34B08
Key Words: Nonlinear boundary conditions; logistic growth; positive solutions.

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Jerome Goddard II
Department of Mathematics, Auburn University Montgomery
Montgomery, AL 36124, USA
email: jgoddard@aum.edu
Ratnasingham Shivaji
Department of Mathematics and Statistics
University of North Carolina Greensboro
Greensboro, NC 27402, USA
email: r_shivaj@uncg.edu

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