Dynamical Response of Networks under External Perturbations Exact Results.pdf

Dynamical Response of Networks under External Perturbations: Exact Results David D. Chinellato1, Marcus A.M. de Aguiar1,2, Irving R. Epstein2,3, Dan Braha2,4 and Yaneer Bar-Yam2 1Instituto de F´ısica ‘Gleb Wataghin’, Universidade Estadual de Campinas, Unicamp 13083-970, Campinas, SP, Brasil 2New England Complex Systems Institute, Cambridge, Massachusetts 02138 3Department of Chemistry, MS015, Brandeis University, Waltham, Massachusetts 02454, USA 4 University of Massachusetts, Dartmouth, Massachusetts 02747 We introduce and solve a general model of dynamic response under external perturbations. This model captures a wide range of systems out of equilibrium including Ising models of physical sys- tems, social opinions, and population genetics. The distribution of states under perturbation and relaxation process reflects two regimes — one driven by the external perturbation, and one driven by internal ordering. These regimes parallel the disordered and ordered regimes of equilibrium physical 7 systems driven by thermal perturbations but here are shown to be relevant for non-thermal and 0 non-equilibrium external influences on complex biological and social systems. We extend our results 0 to a wide range of network topologies by introducing an effective strength of external perturbation 2 by analytic mean-field approximation. Simulations show this generalization is remarkably accurate for many topologies of current interest in describing real systems. v o PACS numbers: 89.75.-k,05.50.+q,05.45.Xt N 9