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On the Stability of Continuous-Time Systems With Stochastic Delay: Applications to Gene Regulatory Circuits

[+] Author Affiliations
Mehdi Sadeghpour, Gábor Orosz

University of Michigan, Ann Arbor, MI

Paper No. DETC2014-35139, pp. V006T10A078; 10 pages
doi:10.1115/DETC2014-35139
From:
  • ASME 2014 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 6: 10th International Conference on Multibody Systems, Nonlinear Dynamics, and Control
  • Buffalo, New York, USA, August 17–20, 2014
  • Conference Sponsors: Design Engineering Division, Computers and Information in Engineering Division
  • ISBN: 978-0-7918-4639-1
  • Copyright © 2014 by ASME

abstract

In this paper the dynamics and stability of a linear system with stochastic delay are investigated. We assume that the delay may take finitely many different values and its dynamics are modeled by a continuous-time Markov chain. Semi-discretization is used to derive the dynamics of the second moment which leads to necessary and sufficient stability conditions for the trivial solution. We apply these results to investigate the stability of the steady state of an auto-regulatory gene-protein network. We demonstrate that stochastic delay may stabilize the system when the corresponding deterministic system with average delay is unstable.

Copyright © 2014 by ASME
Topics: Stability , Circuits , Delays

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