  We recently introduced the joint gramian for combined state and parameter
reduction [C. Himpe and M. Ohlberger. Cross-Gramian Based Combined State and
Parameter Reduction for Large-Scale Control Systems. arXiv:1302.0634, 2013],
which is applied in this work to reduce a parametrized linear time-varying
control system modeling a hyperbolic network. The reduction encompasses the
dimension of nodes and parameters of the underlying control system. Networks
with a hyperbolic structure have many applications as models for large-scale
systems. A prominent example is the brain, for which a network structure of the
various regions is often assumed to model propagation of information. Networks
with many nodes, and parametrized, uncertain or even unknown connectivity
require many and individually computationally costly simulations. The presented
model order reduction enables vast simulations of surrogate networks exhibiting
almost the same dynamics with a small error compared to full order model.
