Quadratic First Integrals of Kinetic Differential Equations

TL;DR

This paper classifies kinetic differential equations based on their ability to possess quadratic first integrals, providing theoretical insights and computational tools, with applications in biology and combustion theory to be explored later.

Contribution

It introduces a classification of kinetic differential equations regarding quadratic first integrals, combining theoretical results with computational methods.

Findings

Identified classes of kinetic equations with quadratic first integrals

Provided examples and trajectory figures for these systems

Discussed connections to other scientific areas and unresolved problems

Abstract

Classes of kinetic differential equations are delineated which do have a quadratic first integral, and classes which can not have one. Example reactions corresponding to the obtained kinetic differential equations are shown, and a few figures showing the trajectories of the corresponding systems are also included. Connections to other areas are mentioned and unsolved problems collected. The new results are theoretical, although computational tools are heavily used. Applications from biology and combustion theory will come later.