@article{8511615,
  abstract     = {{In this paper, we prove the global asymptotic stability of a class of mass action futile cycle networks which includes a model of processive multisite phosphorylation networks. The proof consists of two parts. In the first part, we prove that there is a unique equilibrium in every positive compatibility class. In the second part, we make use of a piecewise linear in rates Lyapunov function in order to prove the global asymptotic stability of the unique equilibrium corresponding to a given initial concentration vector. The main novelty of the paper is the use of a simple algebraic approach based on the intermediate value property of continuous functions in order to prove the uniqueness of equilibrium in every positive compatibility class.}},
  author       = {{Rao, Shodhan}},
  issn         = {{0303-6812}},
  journal      = {{JOURNAL OF MATHEMATICAL BIOLOGY}},
  keywords     = {{Futile cycles,processive multisite phosphorylation,mass action kinetics,intermediate value property,piecewise linear in rates Lyapunov functions,LaSalle's invariance principle,LINEAR COMPARTMENTAL SYSTEMS,CHEMICAL-REACTION NETWORKS,LYAPUNOV FUNCTIONS,CONVERGENCE RESULT,STEADY-STATES,PHOSPHORYLATION,MECHANISMS}},
  language     = {{eng}},
  number       = {{3}},
  pages        = {{709--726}},
  title        = {{Global stability of a class of futile cycles}},
  url          = {{http://doi.org/10.1007/s00285-016-1039-8}},
  volume       = {{74}},
  year         = {{2017}},
}

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