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  1. Ibrahima Ndiaye & Jean-Luc Gouzé (forthcoming). Global Stability of Reversible Enzymatic Metabolic Chains. Acta Biotheoretica.
    We consider metabolic networks with reversible enzymatic reactions. The model is written as a system of ordinary differential equations, possibly with inputs and outputs. We prove the global stability of the equilibrium (if it exists), using techniques of monotone systems and compartmental matrices. We show that the equilibrium does not always exist. Finally, we consider a metabolic system coupled with a genetic network, and we study the dependence of the metabolic equilibrium (if it exists) with respect to concentrations of enzymes. (...)
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  2. Jonathan Rault, Eric Benoît & Jean-Luc Gouzé (forthcoming). Stabilizing Effect of Cannibalism in a Two Stages Population Model. Acta Biotheoretica.
    In this paper we build a prey–predator model with discrete weight structure for the predator. This model will conserve the number of individuals and the biomass and both growth and reproduction of the predator will depend on the food ingested. Moreover the model allows cannibalism which means that the predator can eat the prey but also other predators. We will focus on a simple version with two weight classes or stage (larvae and adults) and present some general mathematical results. In (...)
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  3. Jean-Luc Gouzé (2010). Comparing Boolean and Piecewise Affine Differential Models for Genetic Networks. Acta Biotheoretica 58 (2):217-232.
    Multi-level discrete models of genetic networks, or the more general piecewise affine differential models, provide qualitative information on the dynamics of the system, based on a small number of parameters (such as synthesis and degradation rates). Boolean models also provide qualitative information, but are based simply on the structure of interconnections. To explore the relationship between the two formalisms, a piecewise affine differential model and a Boolean model are compared, for the carbon starvation response network in E. coli . The (...)
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  4. Etienne Farcot & Jean-Luc Gouzé (2009). Periodic Solutions of Piecewise Affine Gene Network Models with Non Uniform Decay Rates: The Case of a Negative Feedback Loop. Acta Biotheoretica 57 (4).
    This paper concerns periodic solutions of a class of equations that model gene regulatory networks. Unlike the vast majority of previous studies, it is not assumed that all decay rates are identical. To handle this more general situation, we rely on monotonicity properties of these systems. Under an alternative assumption, it is shown that a classical fixed point theorem for monotone, concave operators can be applied to these systems. The required assumption is expressed in geometrical terms as an alignment condition (...)
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