Monotonicity in chemical reaction systems

This paper discusses the question of when the dynamical systems arising from chemical reaction networks are monotone, preserving an order induced by some proper cone. The reaction systems studied are defined by the reaction network structure while the kinetics is only constrained very weakly. Necessary and sufficient conditions on cones preserved by these systems are presented. Linear coordinate changes which make a given reaction system cooperative are characterised. Also discussed is when a reaction system restricted to an invariant subspace is cone preserving, even when the system fails to be cone preserving on the whole of phase space. Many of the proofs allow explicit construction of preserved cones. Numerous examples of chemical reaction systems are presented to illustrate the results.

This is an Accepted Manuscript of an article published by Taylor & Francis in Dynamical Systems on Mar 2009, available at: http://www.tandfonline.com/10.1080/14689360802243813