TY - JOUR

T1 - Novel rate equations describing isochronous chemical reactions

AU - Calogero, Francesco

AU - Leyvraz, François

AU - Sommacal, Matteo

PY - 2011

Y1 - 2011

N2 - 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.

AB - 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.

KW - oscillatory chemical reactions

KW - rate equations

KW - isochronous systems

U2 - 10.1007/s10910-010-9784-1

DO - 10.1007/s10910-010-9784-1

M3 - Article

VL - 49

SP - 870

EP - 879

JO - Journal of Mathematical Chemistry

JF - Journal of Mathematical Chemistry

SN - 0259-9791

IS - 4

ER -