American Institute of Mathematical Sciences

Advanced
2010, 7(2): 301-312. doi: 10.3934/mbe.2010.7.301

A kinetic mechanism inducing oscillations in simple chemical reactions networks

Julien Coatléven 1, and  Claudio Altafini 2,

1. 

Laboratoire POEMS, UMR 7231 CNRS/INRIA/ENSTA, INRIA Rocquencourt, B.P. 105 78153, Le Chesnay Cedex, France
2. 

SISSA-ISAS, International School for Advanced Studies, via Beirut 2-4, 34014 Trieste, Italy

Received  January 2009 Revised  September 2009 Published  April 2010

It is known that a kinetic reaction network in which one or more secondary substrates are acting as cofactors may exhibit an oscillatory behavior. The aim of this work is to provide a description of the functional form of such a cofactor action guaranteeing the onset of oscillations in sufficiently simple reaction networks.
Keywords: Hopf bifurcations, Poincaré-Bendixson theorem., Oscillations, Chemical reaction networks.
Mathematics Subject Classification: Primary: 37G15; Secondary: 92C4.
Citation: Julien Coatléven, Claudio Altafini. A kinetic mechanism inducing oscillations in simple chemical reactions networks. Mathematical Biosciences & Engineering, 2010, 7 (2) : 301-312. doi: 10.3934/mbe.2010.7.301
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