### Synchronization in networks with mixed couplings

Igor Belykh

Abstract.
This talk discusses the influence of network structure on
synchronization in dynamical networks with mixed graphs. A mixed graph is
composed of subgraphs, connecting a subnetwork of nodes via one of the
individual oscillator's variables. An illustrative example is a network of
Lorenz systems where some of the nodes are coupled through the x-variable,
some through the y-variable, and some through both. We extend the
connection graph method to derive bounds on the synchronization threshold
in such networks and show that networks with mixed graphs can have
drastically different synchronization properties from networks connected
through the same variables. We will also discuss synchronization in
networks of bursting neurons with mixed excitatory-inhibitory couplings.