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Publications about 'spatially distributed systems'
Articles in journal or book chapters
  1. M.R. Jovanovic, M. Arcak, and E.D. Sontag. A passivity-based approach to stability of spatially distributed systems with a cyclic interconnection structure. IEEE Transactions on Circuits and Systems, Special Issue on Systems Biology, 55:75-86, 2008. Note: Preprint: also arXiv math.OC/0701622, 22 January 2007.[PDF] Keyword(s): MAPK cascades, systems biology, biochemical networks, nonlinear stability, nonlinear dynamics, diffusion, secant condition, cyclic feedback systems.
    Abstract:
    A class of distributed systems with a cyclic interconnection structure is considered. These systems arise in several biochemical applications and they can undergo diffusion driven instability which leads to a formation of spatially heterogeneous patterns. In this paper, a class of cyclic systems in which addition of diffusion does not have a destabilizing effect is identified. For these systems global stability results hold if the "secant" criterion is satisfied. In the linear case, it is shown that the secant condition is necessary and sufficient for the existence of a decoupled quadratic Lyapunov function, which extends a recent diagonal stability result to partial differential equations. For reaction-diffusion equations with nondecreasing coupling nonlinearities global asymptotic stability of the origin is established. All of the derived results remain true for both linear and nonlinear positive diffusion terms. Similar results are shown for compartmental systems.


Conference articles
  1. M.R. Jovanovic, M. Arcak, and E.D. Sontag. Remarks on the stability of spatially distributed systems with a cyclic interconnection structure. In Proceedings American Control Conf., New York, July 2007, pages 2696-2701, 2007. Keyword(s): systems biology, biochemical networks, cyclic feedback systems, spatially distributed systems, secant condition.
    Abstract:
    For distributed systems with a cyclic interconnection structure, a global stability result is shown to hold if the secant criterion is satisfied.



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Last modified: Thu Nov 23 10:40:57 2017
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