Doctorant sous la direction de S. Niculescu

Titre de la thèse: Delay effects : a Journey from Multi-agent Systems to Genetic Networks
Résumé de la thèse: This thesis discusses diverse types of interconnected systems through networks. We address networks of agents with cooperative tasks and propose a new consensus protocol with delays and anticipatory agents. We study the consensus reaching conditions for networks organized under the proposed model. Moreover, we derive some theoretical results, which can apply to a more general class of systems, concerning stability issues when the considered system has multiple imaginary roots. In terms of networks, this situation can correspond to the case of switching topology networks, when the network can even be disconnected at some point. We separately discuss the case of zero characteristic roots, and roots laying on the imaginary axis, except the origin. Finally, we propose a gene network model with a functionality similar to a multiplexer circuit. Thus, we control two outputs with three input signals, and we carry out a stability analysis. We prove the uniqueness and the stability of the network steady states, and validate the continuous and deterministic model with a stochastic model.