Time Delays and the Stability of Dynamical Networks
February 2, 2015
1:00 pm PHG 646
Abstract
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.
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