Chemical Integration of ODEs using Idealized Abstract Solutions

TL;DR

This paper introduces a versatile framework for converting a broad class of ODEs into chemical reaction networks, enabling new biochemical implementations and analysis of complex dynamical systems.

Contribution

It presents a novel inversion method for transforming ODEs into chemical networks, including a detailed theoretical background and simulation results demonstrating its effectiveness.

Findings

Successful simulation of chaotic attractors with new reaction networks

Identification of reaction networks that differ from existing chemical interpretations

Framework's potential for biochemical implementation of ODE integration

Abstract

In this work, we propose a general inversion framework to non-uniquely invert a very large class of ordinary differential equations (ODEs) into chemical reaction networks. A thorough treatment of the relevant chemical reaction network theory from the literature is given. Various simulation results are provided to augment the selection procedure for the inverse framework, where a previously known kineticization strategy is shown to be deterministically excellent but undesirable in chemical simulations. The utility of the framework is verified by simulating reaction network forms of meaningful ODE systems, and their time series are analyzed. In particular, we provide simulations of deterministic chaotic attractors whose newly discovered reaction networks are non-equivalent with any existing chemical interpretations within the literature, as well as presenting exemplary figures which may form a roadmap to the successful biochemical implementation of the integration of ODE systems.