Bifurcations in time-delay fully-connected networks with symmetry
Universidade de São Paulo. Escola Politécnica. São Paulo, Brazil.
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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 . 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 .
© Owned by the authors, published by EDP Sciences, 2014
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