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Equivalence of coupled networks and networks with multimodal frequency distributions: Conditions for the bimodal and trimodal case

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Equivalence of coupled networks and networks with multimodal frequency distributions: Conditions for the bimodal and trimodal case. / Pietras, Bastian; Deschle, Nicolás; Daffertshofer, Andreas.
In: Physical Review E, Vol. 94, No. 5, 052211, 09.11.2016.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Pietras, B, Deschle, N & Daffertshofer, A 2016, 'Equivalence of coupled networks and networks with multimodal frequency distributions: Conditions for the bimodal and trimodal case', Physical Review E, vol. 94, no. 5, 052211. https://doi.org/10.1103/PhysRevE.94.052211

APA

Pietras, B., Deschle, N., & Daffertshofer, A. (2016). Equivalence of coupled networks and networks with multimodal frequency distributions: Conditions for the bimodal and trimodal case. Physical Review E, 94(5), Article 052211. https://doi.org/10.1103/PhysRevE.94.052211

Vancouver

Pietras B, Deschle N, Daffertshofer A. Equivalence of coupled networks and networks with multimodal frequency distributions: Conditions for the bimodal and trimodal case. Physical Review E. 2016 Nov 9;94(5):052211. doi: 10.1103/PhysRevE.94.052211

Author

Pietras, Bastian ; Deschle, Nicolás ; Daffertshofer, Andreas. / Equivalence of coupled networks and networks with multimodal frequency distributions : Conditions for the bimodal and trimodal case. In: Physical Review E. 2016 ; Vol. 94, No. 5.

Bibtex

@article{1e80cab5e0304b4280c7f23636329d22,
title = "Equivalence of coupled networks and networks with multimodal frequency distributions: Conditions for the bimodal and trimodal case",
abstract = "Populations of oscillators can display a variety of synchronization patterns depending on the oscillators' intrinsic coupling and the coupling between them. We consider two coupled symmetric (sub)populations with unimodal frequency distributions. If internal and external coupling strengths are identical, a change of variables transforms the system into a single population of oscillators whose natural frequencies are bimodally distributed. Otherwise an additional bifurcation parameter κ enters the dynamics. By using the Ott-Antonsen ansatz, we rigorously prove that κ does not lead to new bifurcations, but that a symmetric two-coupled-population network and a network with a symmetric bimodal frequency distribution are topologically equivalent. Seeking for generalizations, we further analyze a symmetric trimodal network vis-{\`a}-vis three coupled symmetric unimodal populations. Here, however, the equivalence with respect to stability, dynamics, and bifurcations of the two systems no longer holds.",
author = "Bastian Pietras and Nicol{\'a}s Deschle and Andreas Daffertshofer",
year = "2016",
month = nov,
day = "9",
doi = "10.1103/PhysRevE.94.052211",
language = "English",
volume = "94",
journal = "Physical Review E",
issn = "1539-3755",
publisher = "American Physical Society",
number = "5",

}

RIS

TY - JOUR

T1 - Equivalence of coupled networks and networks with multimodal frequency distributions

T2 - Conditions for the bimodal and trimodal case

AU - Pietras, Bastian

AU - Deschle, Nicolás

AU - Daffertshofer, Andreas

PY - 2016/11/9

Y1 - 2016/11/9

N2 - Populations of oscillators can display a variety of synchronization patterns depending on the oscillators' intrinsic coupling and the coupling between them. We consider two coupled symmetric (sub)populations with unimodal frequency distributions. If internal and external coupling strengths are identical, a change of variables transforms the system into a single population of oscillators whose natural frequencies are bimodally distributed. Otherwise an additional bifurcation parameter κ enters the dynamics. By using the Ott-Antonsen ansatz, we rigorously prove that κ does not lead to new bifurcations, but that a symmetric two-coupled-population network and a network with a symmetric bimodal frequency distribution are topologically equivalent. Seeking for generalizations, we further analyze a symmetric trimodal network vis-à-vis three coupled symmetric unimodal populations. Here, however, the equivalence with respect to stability, dynamics, and bifurcations of the two systems no longer holds.

AB - Populations of oscillators can display a variety of synchronization patterns depending on the oscillators' intrinsic coupling and the coupling between them. We consider two coupled symmetric (sub)populations with unimodal frequency distributions. If internal and external coupling strengths are identical, a change of variables transforms the system into a single population of oscillators whose natural frequencies are bimodally distributed. Otherwise an additional bifurcation parameter κ enters the dynamics. By using the Ott-Antonsen ansatz, we rigorously prove that κ does not lead to new bifurcations, but that a symmetric two-coupled-population network and a network with a symmetric bimodal frequency distribution are topologically equivalent. Seeking for generalizations, we further analyze a symmetric trimodal network vis-à-vis three coupled symmetric unimodal populations. Here, however, the equivalence with respect to stability, dynamics, and bifurcations of the two systems no longer holds.

U2 - 10.1103/PhysRevE.94.052211

DO - 10.1103/PhysRevE.94.052211

M3 - Journal article

VL - 94

JO - Physical Review E

JF - Physical Review E

SN - 1539-3755

IS - 5

M1 - 052211

ER -