Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
2010-07-30
Physical Review Letters 106, 058101 (2011)
Physics
Condensed Matter
Disordered Systems and Neural Networks
4 pages, 3 figures
Scientific paper
10.1103/PhysRevLett.106.058101
The collective dynamics of a network of coupled excitable systems in response to an external stimulus depends on the topology of the connections in the network. Here we develop a general theoretical approach to study the effects of network topology on dynamic range, which quantifies the range of stimulus intensities resulting in distinguishable network responses. We find that the largest eigenvalue of the weighted network adjacency matrix governs the network dynamic range. Specifically, a largest eigenvalue equal to one corresponds to a critical regime with maximum dynamic range. We gain deeper insight on the effects of network topology using a nonlinear analysis in terms of additional spectral properties of the adjacency matrix. We find that homogeneous networks can reach a higher dynamic range than those with heterogeneous topology. Our analysis, confirmed by numerical simulations, generalizes previous studies in terms of the largest eigenvalue of the adjacency matrix.
Larremore Daniel B.
Restrepo Juan G.
Shew Woodrow L.
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