2009-Chellaboina, Vijaysekhar, Sanjay P. Bhat, Wassil M. Haddad, Dennis S. Bernstein - Modeling And Analysis - Mass Action Kinetics.

By Brian Winkel

SIMIODE, Chardon OH USA

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Abstract

Chellaboina, Vijaysekhar, Sanjay P. Bhat, Wassil M. Haddad, Dennis S. Bernstein. 2009. Modeling And Analysis - Mass Action Kinetics. IEEE Control Systems Magazine. August. 60-78.

See https://ieeexplore.ieee.org/document/5184956

From the Introduction:

"Mass-action kinetics are used in chemistry and chemical engineering to describe the dynamics of systems of chemical reactions, that is, reaction networks [1], [2]. These models are a special form of compartmental systems, which involve mass- and energy-balance relations [3]–[5]. Aside from their role in chemical engineering applications, mass-action kinetics have numerous analytical properties that are of inherent interest from a dynamical systems perspective. For example, mass-action kinetics give rise to systems of differential equations having polynomial nonlinearities. Polynomial systems are notorious for their intricate analytical properties even in low-dimensional cases [6]– [10]. Because of physical considerations, however, mass action kinetics have special properties, such as nonnegative solutions, that are useful for analyzing their behavior [11]–[14].

"With this motivation in mind, this article has several objectives. First, we provide a general construction of the kinetic equations based on the reaction laws. We present this construction in a state-space form that is accessible to the systems and control community. This presentation is based on the formulation given in [11] and [15].

"Next, we consider the nonnegativity of solutions to the kinetic equations. Since the kinetic equations govern the concentrations of the species in the reaction network, it is obvious from physical arguments that nonnegative initial conditions must give rise to trajectories that remain in the nonnegative orthant. To demonstrate this fact, we show that the kinetic equations are essentially nonnegative, and we prove that, for all nonnegative initial conditions, the resulting concentrations are nonnegative."

 

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Researchers should cite this work as follows:

  • Brian Winkel (2020), "2009-Chellaboina, Vijaysekhar, Sanjay P. Bhat, Wassil M. Haddad, Dennis S. Bernstein - Modeling And Analysis - Mass Action Kinetics.," https://simiode.org/resources/7231.

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