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Weak Allee
effect, grazing, and S-shaped bifurcation curves
Emily Poole, Bonnie Roberson and Brittany Stephenson
Vol. 5 (2012), No. 2, 133–158
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Abstract |
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We study a one-dimensional reaction-diffusion model arising in population dynamics where the growth rate is a weak Allee type. In particular, we consider the effects of grazing on the steady states and discuss the complete evolution of the bifurcation curve of positive solutions as the grazing parameter varies. We obtain our results via the quadrature method and Mathematica computations. We establish that the bifurcation curve is S-shaped for certain ranges of the grazing parameter. We also prove this occurrence of an S-shaped bifurcation curve analytically. |
Keywords
ordinary differential equations, nonlinear boundary value
problems, grazing, Allee effect, population dynamics
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Mathematical Subject Classification 2010
Primary: 34B15
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Milestones
Received: 8 February 2011
Revised: 26 September 2011
Accepted: 27 September 2011
Published: 27 January 2013
Communicated by John Baxley
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Authors |
| Emily Poole | |
| Department of Mathematics and
Statistics University of Arkansas Fayatteville, AR 72701 United States |
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| Bonnie Roberson | |
| Department of Mathematics and
Statistics Center for Computational Sciences Mississippi State University Mississippi State, MS 39762 United States |
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| Brittany Stephenson | |
| Department of Mathematics and
Statistics Center for Computational Sciences Mississippi State University Mississippi State, MS 39762 United States |
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