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The interaction graph structure of massaction reaction networks
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Domijan, Mirela and Pécou, Élisabeth (2011) The interaction graph structure of massaction reaction networks. Journal of Mathematical Biology . ISSN 03036812
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Official URL: http://dx.doi.org/10.1007/s0028501104620
Abstract
Behaviour of chemical networks that are described by systems of ordinary differential equations can be analysed via the associated graph structures. This paper deals with observations based on the interaction graph which is defined by the signs of the Jacobian matrix entries. Some of the important graph structures linked to network dynamics are signed circuits and the nucleus (or Hamiltonian hooping). We use massaction chemical reaction networks as an example to showcase interesting observations about the aforementioned interaction graph structures. We show that positive circuits and specific nucleus structures (associated to multistationarity) are always present in a great generic class of massaction chemical and biological networks. The theory of negative circuits remains poorly understood, but there is some evidence that they are indicators of stable periodicity. Here we introduce the concept of nonisolated circuits which indicate the presence of a negative circuit.
Item Type:  Submitted Journal Article  

Subjects:  Q Science > QA Mathematics Q Science > QD Chemistry 

Divisions:  Faculty of Science > Centre for Systems Biology  
Library of Congress Subject Headings (LCSH):  Oscillations, Graph theory, Jacobians, Chemical reactions  Mathematical models  
Journal or Publication Title:  Journal of Mathematical Biology  
Publisher:  Springer  
ISSN:  03036812  
Official Date:  20 August 2011  
Dates: 


Identification Number:  10.1007/s0028501104620  
Status:  Peer Reviewed  
Publication Status:  Published  
Description:  Online first 

References:  Albert R, Jeong H, Barabási AL (2000) Errors and attack tolerance of complex networks. Nature 406: 

URI:  http://wrap.warwick.ac.uk/id/eprint/39046 
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