How crucial is small world connectivity for dynamics? (English) Zbl 1185.37188
Summary: We study the dynamical behavior of the collective field of chaotic systems on small world lattices. Coupled neuronal systems as well as coupled logistic maps are investigated. We observe that significant changes in dynamical properties occur only at a reasonably high strength of nonlocal coupling. Further, spectral features, such as signal-to-noise ratio (SNR), change monotonically with respect to the fraction of random rewiring, i.e. there is no optimal value of the rewiring fraction for which spectral properties are most pronounced. We also observe that for small rewiring, results are similar to those obtained by adding small noise.
MSC:
37N25 | Dynamical systems in biology |
05C82 | Small world graphs, complex networks (graph-theoretic aspects) |
92C20 | Neural biology |
References:
[1] | Barabasi A.-L., Science 286 pp 509– |
[2] | DOI: 10.1103/PhysRevLett.89.054101 · doi:10.1103/PhysRevLett.89.054101 |
[3] | DOI: 10.1007/s100510050067 · doi:10.1007/s100510050067 |
[4] | DOI: 10.1103/PhysRevE.67.026104 · doi:10.1103/PhysRevE.67.026104 |
[5] | DOI: 10.1103/PhysRevE.65.036223 · doi:10.1103/PhysRevE.65.036223 |
[6] | DOI: 10.1103/PhysRevE.62.6409 · doi:10.1103/PhysRevE.62.6409 |
[7] | DOI: 10.1103/PhysRevE.65.016209 · doi:10.1103/PhysRevE.65.016209 |
[8] | DOI: 10.1103/PhysRevE.59.R2520 · doi:10.1103/PhysRevE.59.R2520 |
[9] | DOI: 10.1103/PhysRevE.65.055204 · doi:10.1103/PhysRevE.65.055204 |
[10] | DOI: 10.1098/rspb.1984.0024 · doi:10.1098/rspb.1984.0024 |
[11] | DOI: 10.1103/PhysRevE.66.018101 · doi:10.1103/PhysRevE.66.018101 |
[12] | DOI: 10.1103/PhysRevLett.89.280601 · doi:10.1103/PhysRevLett.89.280601 |
[13] | DOI: 10.1103/PhysRevE.65.016201 · doi:10.1103/PhysRevE.65.016201 |
[14] | DOI: 10.1103/PhysRevE.64.056135 · doi:10.1103/PhysRevE.64.056135 |
[15] | DOI: 10.1103/PhysRevLett.86.2909 · doi:10.1103/PhysRevLett.86.2909 |
[16] | DOI: 10.1103/PhysRevLett.84.2758 · doi:10.1103/PhysRevLett.84.2758 |
[17] | DOI: 10.1209/epl/i2001-00263-9 · doi:10.1209/epl/i2001-00263-9 |
[18] | DOI: 10.1103/PhysRevE.67.036118 · doi:10.1103/PhysRevE.67.036118 |
[19] | DOI: 10.1103/PhysRevE.62.7059 · doi:10.1103/PhysRevE.62.7059 |
[20] | DOI: 10.1103/PhysRevE.60.7332 · doi:10.1103/PhysRevE.60.7332 |
[21] | DOI: 10.1103/PhysRevE.63.041104 · doi:10.1103/PhysRevE.63.041104 |
[22] | DOI: 10.1103/PhysRevE.66.016209 · doi:10.1103/PhysRevE.66.016209 |
[23] | DOI: 10.1038/30918 · Zbl 1368.05139 · doi:10.1038/30918 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.