Fundamentals of Systems Analysis and Modeling of Biosystems and Metabolism

Steady-State and Dynamic Characteristics

Author(s): Kazuyuki Shimizu and Yu Matsuoka

Pp: 225-257 (33)

Doi: 10.2174/9781681080864115010009

* (Excluding Mailing and Handling)

Abstract

Once the appropriate model was developed, the steady-state and dynamic characteristics such as multiple steady states and stability etc. can be analyzed. Multiple steady states are analyzed from the point of view of Catastrophy. The dynamic characteristics around the steady state are analyzed based on the perturbation of the state and the stability analysis with phase plane analysis. The bifurcation analysis is briefly explained for the limit cycle bifurcating from the steady state as Hopf-bifurcation. The dynamics of continuous stirred tank fermenter (CSTF) for the different expression of the cell growth rate is explained. The dynamics of the Lotka-Volterra population model is explained. The chaotic behavior is also explained for the simple logistic model.


Keywords: Dynamics, multiple steady states, Catastrrophy theory, phase plane, limit cycle, stability, Hopf-bifurcation, chaos.

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