International audienceIn this article, we consider piecewise affine differential equations modelling gene networks. We work with arbitrary decay rates, and under a local hypothesis expressed as an alignment condition of successive focal points. The interaction graph of the system may be rather complex (multiple intricate loops of any sign, multiple thresholds, etc.). Our main result is an alternative theorem showing that if a sequence of region is periodically visited by trajectories, then under our hypotheses, there exists either a unique stable periodic solution, or the origin attracts all trajectories in this sequence of regions. This result extends greatly our previous work on a single negative feedback loop. We give several examples an...
International audienceThis paper concerns periodic solutions of a class of equations that model gene...
Hybrid systems, and especially piecewise affine (PWA) systems, are often used to model gene regulato...
Hybrid systems, and especially piecewise affine (PWA) systems, are often used to model gene regulato...
International audienceIn this article, we consider piecewise affine differential equations modelling...
International audienceIn this article, we consider piecewise affine differential equations modelling...
International audienceIn this article, we consider piecewise affine differential equations modelling...
In this paper we consider piecewise affine differential equations modeling gene networks. We work wi...
In this paper we consider piecewise affine differential equations modeling gene networks. We work wi...
In this paper we consider piecewise affine differential equations modeling gene networks. We work wi...
International audiencePiecewise affine (PWA) systems are often used to model gene regulatory network...
International audienceThis paper concerns periodic solutions of a class of equations that model gene...
International audiencePiecewise affine (PWA) systems are often used to model gene regulatory network...
International audiencePiecewise affine (PWA) systems are often used to model gene regulatory network...
International audienceThis paper concerns periodic solutions of a class of equations that model gene...
International audienceThis paper concerns periodic solutions of a class of equations that model gene...
International audienceThis paper concerns periodic solutions of a class of equations that model gene...
Hybrid systems, and especially piecewise affine (PWA) systems, are often used to model gene regulato...
Hybrid systems, and especially piecewise affine (PWA) systems, are often used to model gene regulato...
International audienceIn this article, we consider piecewise affine differential equations modelling...
International audienceIn this article, we consider piecewise affine differential equations modelling...
International audienceIn this article, we consider piecewise affine differential equations modelling...
In this paper we consider piecewise affine differential equations modeling gene networks. We work wi...
In this paper we consider piecewise affine differential equations modeling gene networks. We work wi...
In this paper we consider piecewise affine differential equations modeling gene networks. We work wi...
International audiencePiecewise affine (PWA) systems are often used to model gene regulatory network...
International audienceThis paper concerns periodic solutions of a class of equations that model gene...
International audiencePiecewise affine (PWA) systems are often used to model gene regulatory network...
International audiencePiecewise affine (PWA) systems are often used to model gene regulatory network...
International audienceThis paper concerns periodic solutions of a class of equations that model gene...
International audienceThis paper concerns periodic solutions of a class of equations that model gene...
International audienceThis paper concerns periodic solutions of a class of equations that model gene...
Hybrid systems, and especially piecewise affine (PWA) systems, are often used to model gene regulato...
Hybrid systems, and especially piecewise affine (PWA) systems, are often used to model gene regulato...