Stability analysis of non-linear network scillator, neuronal population application
type: Dataset
description: It is widely recognized that rhythmic oscillatory activity in networks of neurons plays an important role in the brain functionning and a key role in processing neural information. This thesis is devoted to the analysis of this synchronized activity by using tools and methods issued from automatic control and stability theory. Two models are used to describe oscillatory activity of neural networks : Kuramoto model and network of Hindmarsh-Rose neurons. First, we consider Kuramoto model with complete (all-to-all) coupling, which is one of the simplest systems used to model neural network. For this model we construct an auxiliary linear system that preserves information on the natural frequencies and interconnection gains of the original Kuramoto model. Next, stability properties of this model are analyzed and we show that the solutions of the new linear system converge to a stable periodic limit cycle. Finally, we show that constrained to the limit cycle, dynamics of the linear system coincide with the original Kuramoto model. Second, a model for the network (population) with a better behavior, with respect to the Kuramoto model, from a biological point of view but more complex is considered. Particularly, we consider a network of diffusively coupled neurons where we use a Hindmarsh-Rose model to describe the dynamics of each individual neuron. Based on semi-passivity of individual Hindmarsh-Rose neurons, we analyse stability properties of a heterogeneous network of such neurons and show that network is practically synchronized for sufficient large values of interconnection gains. Moreover, we characterize the limiting synchronized behavior by using an averaging of all neuron dynamics.
identifier: NNT: 2013PA112236
issued: 2026-05-08T06:04:52.850136
language: fr
modified: 2026-05-08T06:04:52.850141
contact point: Organization
  fn: CCSD
keyword: all-to-all-coupling
keyword: asymptotic-stability-of-linear-systems
keyword: asymptotic-stability-of-non-linear-systems
keyword: comportement-neuronal-oscillatoire
keyword: couplage-complet-all-to-all
keyword: couplage-diffusif
keyword: cycle-limite
keyword: diffusive-coupling
keyword: hindmarsh-rose-neural-model
keyword: infoeu-reposemanticsdoctoralthesis
keyword: kuramoto-model
keyword: limit-cycle
keyword: model-reduction
keyword: modele-de-hindmarsh-rose
keyword: modele-de-kuramoto
keyword: neural-oscillatory-behavior
keyword: physcondcm-genphysics-physicscondensed-matter-cond-matother-cond-matother
keyword: practical-stability-network-of-non-linear-units
keyword: reduction-de-modele
keyword: semi-passivite
keyword: semi-passivity
keyword: stabilite-asymptotique-de-systemes-lineaires
keyword: stabilite-asymptotique-de-systemes-non-lineaires
keyword: stabilite-pratique-de-reseaux-non-lineaires
keyword: synchronisation
keyword: synchronization
keyword: theses
landing page: https://theses.hal.science/tel-00904403

Stability analysis of non-linear network scillator, neuronal population application
type: Distribution
format: HTML
issued: 2026-05-08T06:04:52.852869
modified: 2026-05-08T06:04:52.805723
access URL: https://theses.hal.science/tel-00904403

test_moissonnage_selune
type: Agent