Population Dynamics with Nonlinear Diffusion

Authors

David Perry, New York UniversityFollow
Jessica Schaefer, Northern Arizona UniversityFollow
Brian Schilling, Mississppi State UniversityFollow
Matthew Williams, Clarkson UniversityFollow

Abstract

We consider reaction diffusion models in population dynamics where the per capita growth rate is a logistic type or a weak Allee type. In particular, we study the effects of nonlinear diffusion (arising due to aggregative population movements) on the steady states. We obtain our results via the quadrature method.

Author Bio

David Perry is from New Boston, New Hampshire and is a recent graduate of NewYork University.

Jessica is from Chandler, Arizona. She is a Mathematics and Mathematics Education student at Northern Arizona University. This paper is the result of research conducted under Dr. Ratnasingham Shivaji as part of the Mississippi State University REU 2005 program.

I am a Junior at Mississippi State University pursuing a double major in Aerospace Engineering and Mathematics. David Perry, Jessica Schaefer, Matthew Williams, and I completed this paper as part of a Research Experience for Undergraduates at Mississippi State University under the supervision of Dr. Ratnasingham Shivaji. I am thankful for the opportunity to develop my research skills and to co-author this paper with such wonderful research partners.

Matthew is a student at Clarkson University and is studying biology and mathematics.

Faculty Sponsor

R. Shivaji

Recommended Citation

Perry, David; Schaefer, Jessica; Schilling, Brian; and Williams, Matthew (2006) "Population Dynamics with Nonlinear Diffusion," Rose-Hulman Undergraduate Mathematics Journal: Vol. 7: Iss. 2, Article 1.
Available at: https://scholar.rose-hulman.edu/rhumj/vol7/iss2/1