Transition from amplitude to oscillation death in a network of oscillators

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...

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Bibliographic Details
Published in:Chaos (Woodbury, N.Y.) N.Y.), 2014-12, Vol.24 (4), p.043103-043103
Main Authors: Nandan, Mauparna, Hens, C R, Pal, Pinaki, Dana, Syamal K
Format: Article
Language:English
Subjects:
AMPLITUDES
BIFURCATION
Bifurcations
Broken symmetry
CHAOS THEORY
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
Clusters
LIMIT CYCLE
Links
Mathematical models
MEAN-FIELD THEORY
OSCILLATIONS
OSCILLATORS
Steady state
STEADY-STATE CONDITIONS
SYMMETRY BREAKING
System dynamics
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Summary: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.
ISSN:1054-1500
1089-7682
DOI:10.1063/1.4897446