Stability of small-amplitude periodic solutions near Hopf bifurcations in time-delayed fully-connected PLL networks
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Data
2017-04-01
Autores
Ferruzzo Correa, Diego P.
Bueno, Atila M. [UNESP]
Castilho Piqueira, Jose R.
Título da Revista
ISSN da Revista
Título de Volume
Editor
Elsevier B.V.
Resumo
In this paper we investigate stability conditions for small-amplitude periodic solutions emerging near symmetry-preserving Hopf bifurcations in a time-delayed fully-connected N-node PLL network. The study of this type of systems which includes the time delay between connections has attracted much attention among researchers mainly because the delayed coupling between nodes emerges almost naturally in mathematical modeling in many areas of science such as neurobiology, population dynamics, physiology and engineering. In a previous work it has been shown that symmetry breaking and symmetry preserving Hopf bifurcations can emerge in the parameter space. We analyze the stability along branches of periodic solutions near fully-synchronized Hopf bifurcations in the fixed-point space, based on the reduction of the infinite-dimensional space onto a twodimensional center manifold in normal form. Numerical results are also presented in order to confirm our analytical results. (C) 2016 Elsevier B.V. All rights reserved.
Descrição
Palavras-chave
Time-delay differential equations, Networks, Synchronization, Hopf bifurcation, Stability
Como citar
Communications In Nonlinear Science And Numerical Simulation. Amsterdam: Elsevier Science Bv, v. 45, p. 66-74, 2017.