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

## 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 |
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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: | 10 Aug 2015 11:19 |

URI: | http://nrl.northumbria.ac.uk/id/eprint/6871 |

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