Dynamical Systems Seminar

In real networks the time it takes to send and process information inevitably leads to time delays in the network's dynamics. These time-delays are important to the network's dynamics as they are often the source of instability and poor performance. In this talk we consider the stability of a general class of dynamical networks (collections of interacting dynamical systems). We begin by discussing the underlying graph structure of a network, then present a criteria for the global stability a general class of network. We show that this type of stability is invariant with respect to the addition and removal of specific types of time delays and is therefore stronger than the standard notion of global stability. By using this new notion of stability we show that it is possible to reduce a network by removing its "implicit delays". The resulting lower dimensional network can then be used to obtain improved stability estimates of the original unreduced network. This is joint work with L. A. Bunimovich.