Spectral Coarse Graining and Synchronization in Oscillator Networks
arXiv:0708.2055 · doi:10.1103/PhysRevLett.100.174104
Abstract
Coarse graining techniques offer a promising alternative to large-scale simulations of complex dynamical systems, as long as the coarse-grained system is truly representative of the initial one. Here, we investigate how the dynamical properties of oscillator networks are affected when some nodes are merged together to form a coarse-grained network. Moreover, we show that there exists a way of grouping nodes preserving as much as possible some crucial aspects of the network dynamics. This coarse graining approach provides a useful method to simplify complex oscillator networks, and more generally any network whose dynamics involves a Laplacian matrix.
4 pages, 3 figures
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