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Global stability of a class of futile cycles. (English) Zbl 1361.92027
Summary: 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.

92C40 Biochemistry, molecular biology
34D23 Global stability of solutions to ordinary differential equations
92C45 Kinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.)
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