Asynchronous Networks and Event Driven Dynamics

Real-world networks in physics, biology and technology 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. We make the notion of a functional
asynchronous network rigorous, discuss the phenomenon of dynamical locks, and
present a theorem about the spatiotemporal factorization of the dynamics for a
class of deadlock free functional asynchronous networks of feedforward type. We
conclude with some examples and applications related to asynchronous networks
with a stochastic connection structure.