On Solutions and Heteroclinic Orbits of Some Lotka-Volterra Systems

Abstract

In this work, a principle for getting heteroclinic orbit of a dynamical system has been proposed when the solution is known in a compact form. The proposed principle has been tested through its application to a three species Lotka-Volterra system, which may appear as a mathematical model of human pathogen system. The domain in parameter ( , ) space involve in the model, and the region of initial condition ℍ = {( (0), (0), (0)) ∈ ℝ 3 } ⊂ ℝ 3 for the existence of heteroclinic orbit have been derived.