Novel rate equations describing isochronous chemical reactions

Calogero, Francesco, Leyvraz, François and Sommacal, Matteo (2011) Novel rate equations describing isochronous chemical reactions. Journal of Mathematical Chemistry, 49 (4). pp. 870-879. ISSN 0259-9791

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Official URL: http://dx.doi.org/10.1007/s10910-010-9784-1

Abstract

A simple mathematical model involving two first-order Ordinary Differential Equations (ODEs) with fourth-degree polynomial nonlinearities is introduced. The initial-value problem for this system of two ODEs is solved in terms of elementary functions: for an open set of initial data, this solution is isochronous, i.e., completely periodic with a fixed period (independent of the initial data); in the complementary set of initial data, it blows up at a finite time. This system is likely to be of applicative interest: for instance it models the time evolution of two chemical substances in a spatially homogeneous situation, provided this evolution is characterized by six appropriate chemical reactions whose rates are simply expressed in terms of three a priori arbitrary parameters, or alternatively by five appropriate reactions whose rates are simply expressed in terms of two a priori arbitrary parameters.

Item Type: Article
Uncontrolled Keywords: oscillatory chemical reactions, rate equations, isochronous systems
Subjects: F300 Physics
G100 Mathematics
Department: Faculties > Engineering and Environment > Mathematics and Information Sciences
Depositing User: Ellen Cole
Date Deposited: 09 May 2012 11:36
Last Modified: 10 Aug 2015 11:19
URI: http://nrl.northumbria.ac.uk/id/eprint/6871

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