In this paper, we analyze two possible scenarios for food webs with two prey and one predator (a food web is similar to a food chain except that in a web we have more than one species at some levels). In neither scenario do the prey compete, rather the scenarios differ in the selection method used by the predator. We determine how the dynamics depend on various parameter values. For some parameter values, one or more species dies out. For other parameter values, all species co-exist at equilibrium. For still other parameter values, the populations behave cyclically. We have even discovered parameter values for which the system exhibits chaos and has a positive Lyapunov exponent. Our analysis relies on common techniques such as nullcline analysis, equilibrium analysis and singular perturbation analysis.
Gwendolen Hines - Department of Mathematics and Statistics, University of Nebraska-Lincolnghines@math.unl.eduandBo Deng - Department of Mathematics and Statistics, University of Nebraska-Lincolnbdeng@math.unl.edu
Bockelman, Brian; Green, Elizabeth; Lippitt, Leslie; and Sherman, Jason
"Long Term Dynamics for Two Three-Species Food Webs,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 4
, Article 6.
Available at: http://scholar.rose-hulman.edu/rhumj/vol4/iss2/6