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The existence and classification of synchrony-breaking bifurcations in regular homogenous networks using lattice structures
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Kamei, Hiroko. (2009) The existence and classification of synchrony-breaking bifurcations in regular homogenous networks using lattice structures. International Journal of Bifurcation and Chaos, Vol.19 (No.11). pp. 3707-3732. ISSN 0218-1274
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Official URL: http://dx.doi.org/10.1142/S0218127409025079
Abstract
For regular homogeneous networks with simple eigenvalues (real or complex), all possible explicit forms of lattices of balanced equivalence relations can be constructed by introducing lattice generators and lattice indices [Kamei, 2009]. Balanced equivalence relations in the lattice correspond to clusters of partially synchronized cells in a network. In this paper, we restrict attention to regular homogeneous networks with simple real eigenvalues, and one-dimensional internal dynamics for each cell. We first show that lattice elements with nonzero indices indicate the existence of codimension-one synchrony-breaking steady-state bifurcations, and furthermore, the positions of such lattice elements give the number of partially synchronized clusters. Using four-cell regular homogeneous networks as an example, we then classify a large number of regular homogeneous networks into a small number of lattice structures, in which networks share an equivalent clustering type. Indeed, some of these networks even share the same generic bifurcation structure. This classification leads us to explore how regular homogeneous networks that share synchrony-breaking bifurcation structure are topologically related.
| Item Type: | Journal Article |
|---|---|
| Subjects: | Q Science > QA Mathematics Q Science |
| Divisions: | Faculty of Science > Molecular Organisation and Assembly in Cells (MOAC) |
| Journal or Publication Title: | International Journal of Bifurcation and Chaos |
| Publisher: | World Scientific Publishing Co. Pte. Ltd. |
| ISSN: | 0218-1274 |
| Date: | November 2009 |
| Volume: | Vol.19 |
| Number: | No.11 |
| Number of Pages: | 26 |
| Page Range: | pp. 3707-3732 |
| Identification Number: | 10.1142/S0218127409025079 |
| Status: | Peer Reviewed |
| Publication Status: | Published |
| Access rights to Published version: | Restricted or Subscription Access |
| Funder: | Engineering and Physical Sciences Research Council (EPSRC) |
| Grant number: | EP/D043859 (EPSRC) |
| URI: | http://wrap.warwick.ac.uk/id/eprint/6348 |
Data sourced from Thomson Reuters' Web of Knowledge
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