Korean Journal of Chemical Engineering

, Volume 23, Issue 3, pp 419–427 | Cite as

Undamped oscillations in bacterial glycolysis models



The exotic dynamical behaviors exhibited in chemical reaction systems, such as multiple steady states, undamped oscillations, chaos, and so on, often result from unstable steady states. A bacterial glycolysis model is studied, which involves the generation of adenosine triphosphate (ATP) in a flow system and consists of eight species and ten reactions. A minimum subnetwork of the bacterial glycolysis model is determined to exhibit an unstable steady state with a positive real eigenvalue, which gives rise to undamped oscillations for a small perturbation. A set of rate constants and the corresponding unstable steady state are computed by using a positive real eigenvalue condition. The phenomena of oscillations and bifurcation are discussed. These results are extended to the bacterial glycolysis model and several parent networks.

Key words

Chemical Reaction Network Oscillation Positive Real Eigenvalue Glycolysis Bifurcation 


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Copyright information

© Korean Institute of Chemical Engineering 2006

Authors and Affiliations

  1. 1.Department of Chemical EngineeringNational United UniversityTaiwan, R.O.C.

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