Mapping from structure to dynamics: a unified view of dynamical processes on networks
Jie Zhang1, Changsong Zhou, Xiaoke Xu
1Department of Electronic and Information Engineering, Hong Kong Polytechnic University, Hong Kong, People's Republic of China. jzhang080@gmail.com
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 28, 2010
Summary
We developed a computational method to link network structure to system dynamics, unifying diverse processes like diffusion and neuron firing. This reveals how network features drive functional diversity in complex systems.
Area of Science:
- Complex Systems Science
- Network Science
- Computational Dynamics
Background:
- Network structure fundamentally influences collective dynamics, but the precise relationship remains unclear.
- Understanding this structure-dynamics link is crucial for diverse fields, from neuroscience to epidemiology.
Purpose of the Study:
- To develop a general computational framework for mapping network topology directly to emergent dynamical patterns.
- To unify the understanding of various dynamical processes on networks.
- To define a multiscale complexity measure based on network structure.
Main Methods:
- A general computational transformation to map network topology to dynamical patterns.
- Analysis of diverse dynamical processes including coupled oscillators, neuron firing, epidemic spreading, and diffusion.
- Development of a multiscale complexity measure derived from the structure-dynamics transformation.
Main Results:
- A unified procedure was found applicable to seemingly different dynamical processes on networks.
- The structure-dynamics transformation exhibits inherent multiscale properties.
- Network topological features like modularity, hierarchy, and heterogeneity correlate with higher functional diversity (complexity).
Conclusions:
- Network structure directly dictates emergent dynamical patterns across various processes.
- A novel multiscale complexity measure quantifies functional diversity solely from network topology.
- The evolution of physical network structures is likely driven by the need to support functional diversity.
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