Structural analysis of certain linear operators representing chemical network systems via the existence and uniqueness theorems of spectral resolution. III

✍ Scribed by Shigeru Arimoto; Kenichi Fukui; Hiromu Ohno; Keith F. Taylor; Paul G. Mezey

• Publisher: John Wiley and Sons
• Year: 1997
• Tongue: English
• Weight: 228 KB
• Volume: 63
• Category: Article
• ISSN: 0020-7608
• DOI: 10.1002/(sici)1097-461x(1997)63:1<149::aid-qua18>3.0.co;2-7

✦ Synopsis

By extending the methodology given in Parts I and II of this series of articles, certain dynamical systems of chemical kinetic equations are analyzed in the Ž . setting of the Banach algebra B B B of all bounded operators acting on a Banach space Ž . B B. In this article, we proceed from the general setting of B B B , which played a central role in Part II, toward its specific application to the dynamical systems. In our analysis, Ž . crucial initial steps are taken by i equipping the abstract space B B with the ''positive Ž qn . Ž . quadrant,'' which we denote by ⌫ ‫ޒ‬ , and by ii investigating the asymptotic behavior Ž . Ž . Ž . Ž . Ž qn . of the solution x t of the initial-value problem dx t rdt s Tx t , x 0 s g ⌫ ‫ޒ‬ ;

Ž . B B, where T g B B B is suitably specified for our application purposes. The main theorem and its two specialized versions, together with the notions of ⌫-semipositive operators and semipositive matrices presented here, serve as fundamental tools for the analysis of a class of dynamical systems of chemical kinetic equations whose examples were