Flow analysis and first integrals of a family of 3D Lotka-Volterra Systems

Abstract

Differential equations appear in many interdisciplinary areas, at the interface between mathematics and a variety of fields, from biology and chemistry to economy and physics. They are mathematically studied from several different perspectives, mostly concerned with their solutions, functions that make the equation hold true. In general, not all differential equations admit solutions in terms of elementary functions. Computer simulations and/or the qualitative theory of differential equations are being used to the analyze differential equations whose explicit solutions are hard to find.