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Symmetric bifurcation analysis of synchronous states of time-delayed coupled Phase-Locked Loop oscillators

Ferruzzo Correa, DP, Piqueira, JRC and Wulff, C (2014) Symmetric bifurcation analysis of synchronous states of time-delayed coupled Phase-Locked Loop oscillators Communications in Nonlinear Science and Numerical Simulation.

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Abstract

In recent years there has been an increasing interest in studying time-delayed coupled networks of oscillators since these occur in many real life applications. In many cases symmetry patterns can emerge in these networks, as a consequence a part of the system might repeat itself, and properties of this subsystem are representative of the dynamics on the whole phase space. In this paper an analysis of the second order N-node time-delay fully connected network is presented which is based on previous work: synchronous states in time-delay coupled periodic oscillators: a stability criterion. Correa and Piqueira (2013), for a 2-node network. This study is carried out using symmetry groups. We show the existence of multiple eigenvalues forced by symmetry, as well as the existence of Hopf bifurcations. Three different models are used to analyze the network dynamics, namely, the full-phase, the phase, and the phase-difference model. We determine a finite set of frequencies ω, that might correspond to Hopf bifurcations in each case for critical values of the delay. The S map is used to actually find Hopf bifurcations along with numerical calculations using the Lambert W function. Numerical simulations are used in order to confirm the analytical results. Although we restrict attention to second order nodes, the results could be extended to higher order networks provided the time-delay in the connections between nodes remains equal. © 2014 Elsevier B.V. All rights reserved.

Item Type: Article
Divisions : Faculty of Engineering and Physical Sciences > Mathematics
Authors :
AuthorsEmailORCID
Ferruzzo Correa, DPUNSPECIFIEDUNSPECIFIED
Piqueira, JRCUNSPECIFIEDUNSPECIFIED
Wulff, CUNSPECIFIEDUNSPECIFIED
Date : 2014
Identification Number : 10.1016/j.cnsns.2014.08.004
Additional Information : NOTICE: this is the author’s version of a work that was accepted for publication in Communications in Nonlinear Science and Numerical Simulation. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Communications in Nonlinear Science and Numerical Simulation, August 2014, DOI 10.1016/j.cnsns.2014.08.004.
Depositing User : Symplectic Elements
Date Deposited : 07 Nov 2014 15:32
Last Modified : 19 Feb 2015 02:33
URI: http://epubs.surrey.ac.uk/id/eprint/806395

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