BOOLEAN DELAY EQUATIONS ON NETWORKS IN ECONOMICS AND THE GEOSCIENCES - Coluzzi, Barbara and Ghil, Michael and Hallegatte, Stephane and Weisbuch, Gerard
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS 21, 3511-3548 (2011)
Abstract : We study damage propagation in networks, with an emphasis on
production-chain models. The models are formulated as systems of Boolean
delay equations. This formalism helps take into account the complexity
of the interactions between firms; it turns out to be well adapted to
investigating propagation of an initial damage due to a climatic or
other natural disaster.
We consider in detail the effects of distinct delays and forcing, which
represent external intervention to prevent economic collapse. We also
account for the possible presence of randomness in the links and the
delays. The paper concentrates on two different network structures,
periodic and random, respectively; their study allows one to understand
the effects of multiple, concurrent production paths, and the role
played by the network topology in damage propagation. Applications to
the recent network modeling of climate variability are discussed.