Solvable model for chemical oscillations

Abstract

The Lotka–Volterra equation, proposed first with two variables by A. J. Lotka, underpins the well-known classic model for chemical oscillations. The general solutions of the Lotka–Volterra equation, with $n$ variables, however, remain unknown. We describe a solvable nonlinear model and general solution, previously unstudied for chemical oscillations, that is analogous to the Lotka–Volterra equations with $n$ variables. This model approximates the Lotka–Volterra equations in the neighbourhood of an equilibrium point and is solvable because it can be shown to be linearized to a set of first-order linear differential equations. The purpose of this report is a description of the general solution of the model.