NDLI: Models for Multi-Specie Chemical Reactions Using Polynomial Stochastic Hybrid Systems

Content Provider	IEEE Xplore Digital Library
Author	Singh, A. Hespanha, J.P.
Copyright Year	2005
Description	Author affiliation: Center for Control Engineering and Computation University of California, Santa Barbara, CA 93101. abhi@engineering.ucsb.edu (Singh, A.)
Abstract	A procedure for constructing approximate stochastic models for chemical reactions is presented. This is done by representing the population of various species involved in a chemical reaction as the continuous state of a polynomial Stochastic Hybrid System (pSHS). An important property of pSHSs is that the dynamics of all the statistical moments of its continuous states, evolves according to a infinite-dimensional linear ordinary differential equation (ODE). Under appropriate conditions, this infinite-dimensional ODE can be accurately approximated by a finite-dimensional nonlinear ODE, the state of which typically contains the moments of interest. In this paper, for a very general class of chemical reactions, we provide existence and uniqueness conditions for these finite-dimensional nonlinear ODEs. Furthermore, explicit formulas to construct them are also provided. To illustrate the applicability of our results, we construct an approximate stochastic model for a decaying and dimerizing chemical reaction set. Moment estimates obtained from the finite-dimensional nonlinear ODE are compared with estimates obtained from a large number of Monte Carlo simulations.
Starting Page	2969
Ending Page	2974
File Size	278209
Page Count	6
File Format	PDF
ISBN	0780395670
DOI	10.1109/CDC.2005.1582616
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2005-12-15
Publisher Place	Spain
Access Restriction	Subscribed
Rights Holder	IEEE/EUCA
Subject Keyword	Chemicals Polynomials Stochastic systems Stochastic processes Differential equations Vectors Nonlinear dynamical systems Kinetic theory Probability density function Biological materials
Content Type	Text
Resource Type	Article

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