Seminar of Differential Equations and Dynamic Systems - Mihály Pituk (21.5.2019)
[Translate to English:] v utorok 21.5.2019 o 14:00 hod. v miestnosti M/109
By: František Jaroš
prof. Mihály Pituk (Department of Mathematics, University of Pannonia, Veszprém, HUNGARY):
Semistability of complex balanced kinetic systems with time delays
In this talk we introduce a class of delayed kinetic systems derived from mass action type reaction network models. We define the time delayed positive stoichiometric compatibility classes and the notion of complex balanced time delayed kinetic systems. We prove the existence and uniqueness of equilibria within the time delayed positive stoichiometric compatibility classes. We prove the semistability of the equilibria for time delayed complex balanced sytems using an appropriate Lyapunov-Krasovskii functional and LaSalle's invariance principle. As a consequence, we show that every positive complex balanced equilibrium is locally asymptotically stable relative to its positive stoichiometric compatibility class.
The talk is based on a joint work with Katalin M. Hangos, György Lipták and Gábor Szederkényi from the Institute for Computer Science and Control, Hungarian Academy of Sciences, Budapest, Hungary.