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Weak synchronization and convergence in coupled genetic regulatory networks: Applications to damped oscillators and multistable circuits
Author(s) -
Augier Nicolas,
Chaves Madalena,
Gouzé JeanLuc
Publication year - 2023
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.6061
Subject(s) - synchronization (alternating current) , coupling (piping) , homogeneous , convergence (economics) , stability (learning theory) , topology (electrical circuits) , control theory (sociology) , interconnection , coupling strength , computer science , steady state (chemistry) , stability theory , synchronization networks , state (computer science) , statistical physics , mathematics , nonlinear system , control (management) , physics , engineering , telecommunications , artificial intelligence , algorithm , chemistry , condensed matter physics , machine learning , mechanical engineering , combinatorics , economics , economic growth , quantum mechanics
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.