Uncertain Chemical Kinetics Equations

A central concept of chemical kinetics is reaction rate which describes the dynamic behavior of each molecule in chemical reaction.Assuming environmental factors re-main unchanged,conventional chemical kinetics uses ordinary differential equations to describe the dynamic behavior of each molecule based on the law of mass action.Sig-nificantly,actual chemical reaction is always influenced by environmental factors,called noise.For example,many reactions have endothermic or exothermic phenomena,thus the temperature in the reaction process is not a constant.In other words,environmen-tal factors inevitably fluctuate,and the reaction rate does not completely follow the law of mass action.Stochastic chemical kinetics describes noise in terms of Weiner process,and further derives some stochastic differential equations with respect to molecular con-centration.However,paradoxes occur when stochastic differential equations are used to describe real quantities.In this case,it is necessary to introduce new tool to describe noise in chemical reaction.In this paper,uncertain differential equations are applied to chemical kinetics for the first time.And the derived equations describe the dynamic behavior of each molecule in chemical reaction.For different types of chemical reactions,the change law of molecular concentration is essentially different.It is necessary to establish the corresponding type of uncertain chemical reaction equation.Three types of chemical reaction are considered in this paper: single reactions,parallel reactions with one reactant,and single reactions with delays.One index above reaction rate is half-life of reaction.In the sense of uncer-tain measure,the distribution function of half-life of reaction is derived so as to provide a better understanding of reaction rate.When a set of observation is obtained,the un-known parameters in the uncertain chemical reaction equation can be estimated.In order to improve the accuracy of estimation,a new difference scheme,called Milstein scheme,is derived.In general,this paper mainly has the following innovations and contributions:· Uncertain differential equations are first used to describe the dynamic behavior of molecular concentration in chemical reaction,and then uncertain chemical reaction equations for three types of reactions are established;· Half-life of reaction is introduced,and then the analytical solution or numerical solution of the uncertain distribution of half-life of reaction are given;· The Milstein scheme of uncertain differential equations is derived and applied to estimating the unknown parameters of equations.