Global Stability of Dynamical Networks
In this talk we consider the stability of a general class of
dynamical networks. We begin by giving a brief introduction into the study
of networks including their graph-theoretic structure and the variety if
dynamics such systems exhibit. Following this, we present a criteria for
the global stability of a general dynamical network and show that this type
of stability is invariant with respect to the addition of time delays.
Since time delays can have a destabilizing effect on a system's dynamics
this gives us a stronger form of stability, which we call intrinsic
stability. Additionally, this technique of adding and removing time delays
allows us to collapse a network, in a number of ways, that can be used to
obtain improved stability estimates of the original network.