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.
Solvable model Chemical oscillation Lotka–Volterra equation Nonlinear differential equation
Mathematics Subject Classification
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We thank Yohei Nanazawa for discussions concerning our study. The numerous numerical simulations performed using the RIKEN Integrated Cluster of Clusters (RICC) improved the simulations performed for this study.