Modelling and stability analysis of complex balanced kinetic systems with distributed time delays

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Abstract

Kinetic systems are positive polynomial systems that can be equipped with discrete and/or distributed time delays for describing process models often appearing in complex reaction kinetic systems. Mathematically these models are in the form of delay-differential equations with discrete and/or distributed time delays. The origin of the delays may be an inherent phenomena or some approximation of the biochemical system model. It is shown in the paper that even the simplest transport mechanism, the spatially distributed convection combined with chemical reaction is resulted in a delayed chemical reaction network model, where the parameters of the transport are analytically related to the parameters of the induced delay – discrete for the plug flow and distributed for the laminar flow – in the model. We proved that – similarly to the case of kinetic systems without delay – every positive complex balanced equilibrium of a time delayed kinetic system with arbitrary nondecreasing cumulative delay distribution function is locally asymptotically stable relative to its positive stoichiometric compatibility class. The results and notations were illustrated on a simple example using simulation investigations.

Original languageEnglish
Pages (from-to)13-23
Number of pages11
JournalJournal of Process Control
Volume84
DOIs
Publication statusPublished - Dec 2019

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Keywords

  • Chemical reaction networks
  • Kinetic systems
  • Nonnegative systems
  • Stability theory
  • Time delay

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modelling and Simulation
  • Computer Science Applications
  • Industrial and Manufacturing Engineering

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