TY - JOUR
T1 - A multi-time-scale analysis of chemical reaction networks
T2 - I. Deterministic systems
AU - Lee, Chang Hyeong
AU - Othmer, Hans G.
PY - 2010/9
Y1 - 2010/9
N2 - We consider deterministic descriptions of reaction networks in which different reactions occur on at least two distinct time scales. We show that when a certain Jacobian is nonsingular there is a coordinate system in which the evolution equations for slow and fast variables are separated, and we obtain the appropriate initial conditions for the transformed system. We also discuss topological properties which guarantee that the nonsingularity condition is satisfied, and show that in the new coordinate frame the evolution of the slow variables on the slow time scale is independent of the fast variables to lowest order in a small parameter. Several examples that illustrate the numerical accuracy of the reduction are presented, and an extension of the reduction method to three or more time scale networks is discussed.
AB - We consider deterministic descriptions of reaction networks in which different reactions occur on at least two distinct time scales. We show that when a certain Jacobian is nonsingular there is a coordinate system in which the evolution equations for slow and fast variables are separated, and we obtain the appropriate initial conditions for the transformed system. We also discuss topological properties which guarantee that the nonsingularity condition is satisfied, and show that in the new coordinate frame the evolution of the slow variables on the slow time scale is independent of the fast variables to lowest order in a small parameter. Several examples that illustrate the numerical accuracy of the reduction are presented, and an extension of the reduction method to three or more time scale networks is discussed.
KW - Chemical reaction networks
KW - Multi-time-scale analysis
KW - Reduction of graph of reaction networks
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U2 - 10.1007/s00285-009-0269-4
DO - 10.1007/s00285-009-0269-4
M3 - Article
C2 - 19350241
AN - SCOPUS:73249116652
SN - 0303-6812
VL - 60
SP - 387
EP - 450
JO - Journal of Mathematical Biology
JF - Journal of Mathematical Biology
IS - 3
ER -