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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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, Physics and Electrical Engineering
Depositing User:	Ellen Cole
Date Deposited:	09 May 2012 11:36
Last Modified:	13 Oct 2019 00:31
URI:	http://nrl.northumbria.ac.uk/id/eprint/6871

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