Special Session 13: Nonlinear differential and difference equations with applications to population dynamics
Analysis of a competitive reaction-diffusion population dynamics model with density dependent dispersal on the boundary
Ananta Acharya
University of North Carolina Greensboro
USA
Co-Author(s):    S. Bandyopadhyay, J. Goddard II, A. Muthunayake & R. Shivaji
Abstract:
We study a competitive reaction-diffusion population dynamics model with density dependent dispersal on the boundary. To analyze the model using computational methods in one dimension we take positive and negative density dependent dispersals separately. Namely, for positive density dependent dispersal case, we take $h(u) = 1 + \varepsilon u$ and for negative case we take $h(u) = \frac{1}{1 + \varepsilon u}$. We obtain bifurcation curves using the combination of quadrature method and shooting method for various values of $\varepsilon$ in each case.
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