Existence of periodic solutions for enzyme-catalysed reactions with periodic substrate input

TL;DR

This paper establishes a necessary and sufficient condition for the existence of periodic solutions in enzyme-catalysed reactions with periodically varying substrate input, using topological degree theory.

Contribution

It provides a novel theoretical criterion for periodic solutions in enzyme reactions with periodic substrate input, employing Leray-Schauder degree methods.

Findings

Derived a necessary and sufficient condition for periodic solutions.

Applied Leray-Schauder degree to reaction equations.

Extended understanding of enzyme reaction dynamics with periodic inputs.

Abstract

Considering a basic enzyme-catalysed reaction, in which the rate of input of the substrate varies periodically in time, we give a necessary and sufficient condition for the existence of a periodic solution of the reaction equations. The proof employs the Leray-Schauder degree, applied to an appropriately constructed homotopy.