The Existence of Periodic Orbits in a Particular Form of Homogeneous Lotka Volterra Systems
by
Willard Keeran
University of Florida, Department of Mathematics

A particular type of closed, finite, homogeneous Lotka Volterra system is examined. Using level surfaces and a reduction of order, periodic orbits are shown to exist if the order of the system is a multiple of three or four. Through a perturbation technique, a variable transformation using Fourier matrices, and a result on the rationality of quotients of the roots of unity, it is demonstrated that periodic orbits are not possible if the system's order is a prime number greater than three.

Date received: February 13, 2009