Transition from amplitude to oscillation death in a network of oscillators

Mauparna Nandan, C. R. Hens, Pinaki Pal, Syamal K. Dana

Research output: Contribution to journalArticlepeer-review

32 Scopus citations

Abstract

We report a transition from a homogeneous steady state (HSS) to inhomogeneous steady states (IHSSs) in a network of globally coupled identical oscillators. We perturb a synchronized population of oscillators in the network with a few local negative or repulsive mean field links. The whole population splits into two clusters for a certain number of repulsive mean field links and a range of coupling strength. For further increase of the strength of interaction, these clusters collapse into a HSS followed by a transition to IHSSs where all the oscillators populate either of the two stable steady states. We analytically determine the origin of HSS and its transition to IHSS in relation to the number of repulsive mean-field links and the strength of interaction using a reductionism approach to the model network. We verify the results with numerical examples of the paradigmatic Landau-Stuart limit cycle system and the chaotic Rössler oscillator as dynamical nodes. During the transition from HSS to IHSSs, the network follows the Turing type symmetry breaking pitchfork or transcritical bifurcation depending upon the system dynamics.

Original languageEnglish
Article number043103
JournalChaos
Volume24
Issue number4
DOIs
StatePublished - 17 Oct 2014
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2014 AIP Publishing LLC.

Fingerprint

Dive into the research topics of 'Transition from amplitude to oscillation death in a network of oscillators'. Together they form a unique fingerprint.

Cite this