The decoupling and solution of logistic and classical two-species Lotka-Volterra dynamics with variable production rates

Abstract

<jats:p> Central to the dynamics of population biology are various versions of the Lotka-Volterra equations. Particular cases may be used to model competitive, commensal, predatory and other behaviour. Similar equations describe macro-economic interactions, epidemics and other processes of mass action. Refinements of many versions of these equations have been exhibited in the BIOMAT meetings to describe new biological features. The solutions to such equations may display a variety of forms. Broadly speaking, quite a lot of qualitative information may often be obtained about the solutions. In many cases it is convenient to eliminate time from the equations, so obtaining equations for the joint values of population sizes. By contrast, determining explicit expressions for the evolution with time of the component population sizes frequently appears to be infeasible, although numerical procedures may be available. </jats:p>