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Title: 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 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.
Authors:
 [1] ;  [2] ; ;  [3] ;  [4]
  1. Dr. B. C. Roy Engineering College, Durgapur 713206 (India)
  2. (India)
  3. CSIR-Indian Institute of Chemical Biology, Jadavpur, Kolkata 700032 (India)
  4. Department of Mathematics, National Institute of Technology, Durgapur 713209 (India)
Publication Date:
OSTI Identifier:
22351001
Resource Type:
Journal Article
Resource Relation:
Journal Name: Chaos (Woodbury, N. Y.); Journal Volume: 24; Journal Issue: 4; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; AMPLITUDES; BIFURCATION; CHAOS THEORY; LIMIT CYCLE; MEAN-FIELD THEORY; OSCILLATIONS; OSCILLATORS; STEADY-STATE CONDITIONS; SYMMETRY BREAKING