%0 Conference Proceedings
%4 sid.inpe.br/mtc-m21b/2016/12.20.18.00
%2 sid.inpe.br/mtc-m21b/2016/12.20.18.00.43
%T Synchronization and control in networks with strongly delayed couplings
%D 2016
%A Maia, Daniel,
%A Macau, Elbert Einstein Nehrer,
%@affiliation
%@affiliation Instituto Nacional de Pesquisas Espaciais (INPE)
%@electronicmailaddress
%@electronicmailaddress elbert.macau@inpe.br
%B Workshop de Computação Aplicada, 16 (WORCAP)
%C São José dos Campos, SP
%8 25-26 out.
%X The main purpose of the manuscript is to investigate the synchronization in networks of dynamical systems with strongly delayed connections. We obtain several strict conditions for synchronization of equilibria and periodic solutions by studying their linear stability. We also study how different types of networks influence the synchronization. Considering some regular net- works, as well as more complex heterogeneous and homogeneous networks, we show that it is more difficult to synchronize the heterogeneous networks with long-delayed connections, unless the coupling parameter scales with the total number of nodes. We derive the natural scaling of the coupling parameters, which allows for a synchronization. In networks with instantaneous self-connections, we show that it is possible to stabilize synchronous solutions that are unstable in an isolated system. We study in detail such a control close to a Hopf bifurcation and obtain strict conditions for the stability. In particular, it is shown that the stabilization domains in parameter space are reappearing periodically and decreasing in size with the increase of time-delays. We show how the frequency of the reappearance of the control domains is influenced by the number of cycle multipartitions of the graph.
%@language en
%3 maia_synchronization.pdf