Chemical Reaction Systems with a Homoclinic Bifurcation: an Inverse Problem

TL;DR

This paper introduces an inverse problem framework for designing reaction systems with specific dynamic properties, enabling the construction of bistable systems with homoclinic bifurcations through polynomial ODE transformations.

Contribution

It presents a novel framework that maps polynomial ODEs to reaction networks, facilitating the design of systems with desired bifurcation behaviors.

Findings

Constructed bistable reaction systems with homoclinic bifurcations.

Analyzed phase space topology of the designed systems.

Demonstrated the framework's ability to generate systems with prescribed properties.

Abstract

An inverse problem framework for constructing reaction systems with prescribed properties is presented. Kinetic transformations are defined and analysed as a part of the framework, allowing an arbitrary polynomial ordinary differential equation to be mapped to the one that can be represented as a reaction network. The framework is used for construction of specific two- and three-dimensional bistable reaction systems undergoing a supercritical homoclinic bifurcation, and the topology of their phase spaces is discussed.