Novel rate equations describing isochronous chemical reactions

Francesco Calogero, François Leyvraz, Matteo Sommacal

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1 Citation (Scopus)


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.
Original languageEnglish
Pages (from-to)870-879
JournalJournal of Mathematical Chemistry
Issue number4
Publication statusPublished - 2011


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