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Weak synchronization and convergence in coupled genetic regulatory networks: Applications to damped oscillators and multistable circuits

Nicolas Augier 1, 2 Madalena Chaves 1, 2 Jean-Luc Gouzé 1, 2 
1 BIOCORE - Biological control of artificial ecosystems
CRISAM - Inria Sophia Antipolis - Méditerranée , LOV - Laboratoire d'océanographie de Villefranche, INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement
Abstract : The study of synchronization in coupled genetic networks is a very challenging topic that is usually analyzed on a case-by-case basis. Here we consider a general model of genetic networks and examine two forms of interconnection, either homogeneous or heterogeneous coupling, corresponding to coupling functions that are either equal or different from those governing the individual dynamics. In the case of individual subsystems having unique but different steady states, we prove that the homogeneous coupled system has a unique globally asymptotically stable steady state. Moreover, in the case of large coupling strength, we show that under suitable assumptions the network achieves weak synchronization in the sense that the individual steady states become arbitrarily close. In the heterogeneous case, stability conditions are more intricate and some stronger assumptions on the individual dynamics have to be made, under which we prove a similar weak synchronization result in the case of large coupling strength. We apply the results to the synchronization of damped oscillators and to the control of multistable systems.
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https://hal.inria.fr/hal-03270268
Contributor : Jean-Luc Gouzé Connect in order to contact the contributor
Submitted on : Thursday, June 24, 2021 - 4:15:34 PM
Last modification on : Friday, June 3, 2022 - 3:17:16 AM
Long-term archiving on: : Saturday, September 25, 2021 - 6:44:37 PM

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  • HAL Id : hal-03270268, version 1

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Nicolas Augier, Madalena Chaves, Jean-Luc Gouzé. Weak synchronization and convergence in coupled genetic regulatory networks: Applications to damped oscillators and multistable circuits. International Journal of Robust and Nonlinear Control, Wiley, 2022. ⟨hal-03270268⟩

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