Reduction of Complexity via Operatorial Parametric Formulations for Some Nonlinear Dynamic Problems of Biology

Dynamic models most of the time involve differential equations, which are "time-local". Such models can also be considered "globally", that is in the sense of "trajectories" in the "space-time" state. Up to adapted concepts, such a different interpretation rev...

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Bibliographic Details
Main Authors: Montseny, E., Doncescu, A.
Format: Conference Proceeding
Language:English
Subjects:
Biochemistry
Biological control systems
Biological system modeling
Bioreactors
Computational biology
Couplings
Differential equations
Mathematical model
Nonlinear equations
State-space methods
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Summary:Dynamic models most of the time involve differential equations, which are "time-local". Such models can also be considered "globally", that is in the sense of "trajectories" in the "space-time" state. Up to adapted concepts, such a different interpretation reveals itself more flexible, namely because it allows to use various operatorial transformations whose time-local equivalent in general cannot exist and from which can result some remarkable properties. Namely, we introduce a principle of parametrizing for dynamic equations by means of such transformations. We then consider an example of bioreactor model for which we highlight how suitable time-nonlocal transformations can sometimes be used to efficiently solve some nonlinear control problems.
DOI:10.1109/WAINA.2008.326