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Title: Mapping from structure to dynamics : a unified view of dynamical processes on networks
Authors: Zhang, J
Zhou, C
Xu, X
Small, M
Issue Date: 27-Aug-2010
Source: Physical review. E, Statistical, nonlinear, and soft matter physics, Aug. 2010, v. 82, no. 2, 026116, p. 1-7
Abstract: Although it is unambiguously agreed that structure plays a fundamental role in shaping the collective dynamics of complex systems, how structure determines dynamics exactly still remains unclear. We investigate a general computational transformation by which we can map the network topology directly to the dynamical patterns emergent on it—independent of the nature of the dynamical processes. Remarkably, we find that many seemingly different dynamical processes on networks, such as coupled oscillators, ensemble neuron firing, epidemic spreading and diffusion can all be understood and unified through this same procedure. Utilizing the inherent multiscale nature of this structure-dynamics transformation, we further define a multiscale complexity measure, which can quantify the functional diversity a general network can support at different organization levels using only its structure. We find that a wide variety of topological features observed in real networks, such as modularity, hierarchy, degree heterogeneity and mixing all result in higher complexity. This result suggests that the demand for functional diversity is driving the structural evolution of physical networks.
Keywords: Complex networks
Nonlinear dynamical systems
Topology
Publisher: American Physical Society
Journal: Physical review. E, Statistical, nonlinear, and soft matter physics 
ISSN: 1539-3755
EISSN: 1550-2376
DOI: 10.1103/PhysRevE.82.026116
Rights: Physical Review E © 2010 The American Physical Society. The Journal's web site is located at http://pre.aps.org/
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