Journal of Mathematical Chemistry

, Volume 50, Issue 5, pp 1111–1125 | Cite as

Oscillations in non-mass action kinetics models of biochemical reaction networks arising from pairs of subnetworks

  • Maya Mincheva
Original Paper


It is well known that oscillations in models of biochemical reaction networks can arise as a result of a single negative cycle. On the other hand, methods for finding general network conditions for potential oscillations in large biochemical reaction networks containing many cycles are not well developed. A biochemical reaction network with any number of species is represented by a simple digraph and is modeled by an ordinary differential equation (ODE) system with non-mass action kinetics. The obtained graph-theoretic condition generalizes the negative cycle condition for oscillations in ODE models to the existence of a pair of subnetworks, where each subnetwork contains an even number of positive cycles. The technique is illustrated with a model of genetic regulation.


Biochemical reaction networks Non-mass action kinetics Oscillations Negative feedback cycle 


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© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Department of Mathematical SciencesNorthern Illinois UniversityDeKalbUSA

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