Weak Allee effect, grazing, and S-shaped bifurcation curves

Emily Poole, Bonnie Roberson, Brittany Stephenson
2012 Involve. A Journal of Mathematics  
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
more » ... ameter. We also prove this occurrence of an S-shaped bifurcation curve analytically. MSC2010: 34B15.
doi:10.2140/involve.2012.5.133 fatcat:ihi2acmrpbdfhapvw2f3mnqora