STABILITY OF O.D.E. SYSTEMS ASSOCIATED WITH FIRST ORDER CHEMICAL KINETICS MECHANISMS WITH AND WITHOUT FINAL PRODUCTS

Authors : Victor MARTINEZLUACES

Pages : 80-87

View : 22 | Download : 15

Publication Date : 2016-04-01

Article Type : Research Paper

Abstract :First order chemical reaction mechanisms are modelled through Ordinary Di erential Equations insert ignore into journalissuearticles values(O.D.E.); systems of the form: :X = AX , be- ing X the chemical species concentrations vector, :X its time derivative and A the associated system matrix. In previous papers, First Order Chemical Ki- netics Mechanisms insert ignore into journalissuearticles values(F.O.C.K.M.); involving two or three chemical species were considered and in all these cases, solutions show a weak stability insert ignore into journalissuearticles values(i.e., they are stable but not asymptotically);. This fact implies that small errors due to mea- surements in the initial concentrations will remain bounded, but they do not tend to vanish as the reaction proceeds. In order to know if these results can be extended or not to other chemical mechanisms, a general result is obtained through an inverse modelling approach. For this purpose, theoretical mecha- nisms with and without nal products are proposed, and the corresponding F.O.C.K.M. matrices are studied. As a consequence of the particular structure of the F.O.C.K.M. matrices, the Gershgorin Circles Theorem can be applied to show that all the eigenvalues have real parts negative or zero. Moreover, it is proved as the main result of the paper, that for the null eigenvalue, alge- braic and geometric multiplicities insert ignore into journalissuearticles values(A.M. and G.M.); give the same number. As an application of these results, several conclusions about the stability of the O.D.E. solutions are obtained for this kind of chemical reactions, and its con- sequences on the propagation of concentrations and/or surface concentrations measurement errors are analyzed.
Keywords : Chemical mechanisms, O D E linear systems, Solutions stability