Abstract
Real-world networks in technology, engineering and biology
often exhibit dynamics that cannot be adequately reproduced using network
models given by smooth dynamical systems and a fixed network topology.
Asynchronous networks give a theoretical and conceptual framework for
the study of network dynamics where nodes can
evolve independently of one another, be constrained, stop, and later
restart, and where the interaction between different components of the
network may depend on time, state, and stochastic effects. This
framework is sufficiently general to encompass a wide range of
applications ranging from engineering to neuroscience. Typically, dynamics is piecewise smooth
and there are relationships with Filippov systems.
In the first part of the paper, we give examples of asynchronous networks,
and describe the basic formalism and structure. In the second part,
we make the notion of a functional asynchronous network
rigorous, discuss the phenomenon of dynamical locks, and present a
foundational result on the spatiotemporal factorization of the dynamics
for a large class of functional asynchronous networks.
e-mail: mikefield@gmail.com
Professor Mike Field
Department of Mathematics
Imperial College
London