| Issue |
MATEC Web of Conferences
Volume 16, 2014
CSNDD 2014 - International Conference on Structural Nonlinear Dynamics and Diagnosis
|
|
|---|---|---|
| Article Number | 05005 | |
| Number of page(s) | 3 | |
| Section | Deterministic and stochastic dynamics and control of nonlinear systems | |
| DOI | https://doi.org/10.1051/matecconf/20141605005 | |
| Published online | 01 September 2014 | |
Bifurcations in time-delay fully-connected networks with symmetry
Universidade de São Paulo. Escola Politécnica. São Paulo, Brazil.
a e-mail: dferruzzo@usp.br
In this work a brief method for finding steady-state and Hopf bifurcations in a (R + 1)-th order N-node time-delay fully-connected network with symmetry is explored. A self-sustained Phase-Locked Loop is used as node. The irreducible representations found due to the network symmetry are used to find regions of time-delay independent stability/instability in the parameter space. Symmetry-preserving and symmetry-breaking bifurcations can be computed numerically using the Sn map proposed in [1]. The analytic results show the existence of symmetry-breaking bifurcations with multiplicity N − 1. A second-order N-node network is used as application example. This work is a generalization of some results presented in [2].
© Owned by the authors, published by EDP Sciences, 2014
This is an Open Access article distributed under the terms of the Creative Commons Attribution License 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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