On the synchronization and desynchronization of dynamical systems. Applications
type: Dataset
description: This thesis deals with the synchronization and desynchronization of dynamical systems. In a first part we tackle (under a biological viewpoint) the desynchronization problem, which consists in the induce- ment of a chaotic behavior in a stable dynamical system. We study this problem on a gene regulatory network called V-system, invented in order to couple in a very simple way, a Hopf bifurcation and a hysteresis-type dynamics. After having proved that a vector field on Rn admitting such a coupling may, under some condi- tions, show a chaotic dynamics, we give a set of parameters for which the associated V-system satisfies these conditions and verify numerically that the mechanism responsible of the chaotic motion occurs in this system. In a second part, we take interest in the synchronization of hierarchically organized dynamical systems. We first define a hierarchical structure for a set of 2^n systems by a matrix representing the steps of a matching process in groups of size two. This leads us naturally to the case of a Cantor set of systems, for which we obtain a global synchronization result generalizing the finite case. Finally, we deal with the situation where some defects appear in the hierarchy, that is to say when some links between certain systems are broken. We prove we can afford an infinite number of such broken links while keeping a local synchronization, providing they are only present at the first N stages of the hierarchy (for a fixed integer N) and they are enough spaced out in these stages.
landing page: https://theses.hal.science/tel-00912343
identifier: NNT: 2013NICE4041
keyword: bifurcations
keyword: chaos
keyword: dynamical-systems
keyword: gene-regulatory-networks
keyword: infoeu-reposemanticsdoctoralthesis
keyword: mathmath-gmmathematics-mathgeneral-mathematics-mathgm
keyword: reseaux-de-regulation-genetique
keyword: synchronisation
keyword: synchronization
keyword: systemes-dynamiques
keyword: theses
issued: 2026-05-08T00:22:28.919739
modified: 2026-05-08T00:22:28.919743
language: en
contact point: Organization
  fn: CCSD

test_moissonnage_selune
type: Agent

On the synchronization and desynchronization of dynamical systems. Applications
type: Distribution
format: HTML
access URL: https://theses.hal.science/tel-00912343
issued: 2026-05-08T00:22:28.928856
modified: 2026-05-08T00:22:28.908045