Transition from amplitude to oscillation death in a network of oscillators
arXiv:1409.8071 · doi:10.1063/1.4897446
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 in the network with a few local negative mean field links. It is observed that the whole population splits into two clusters for a certain number of negative mean field links and specific range of coupling strength. For further increases of the strength of interaction these clusters collapse to a HSS followed by a transition to IHSSs. We analytically determine the origin of HSS and its transition to IHSS in relation to the number of negative mean-field links and the strength of interaction using a reductionism approach to the model network in a two-cluster state. We verify the results with numerical examples of networks using the paradigmatic Landau-Stuart limit cycle system and the chaotic Rossler 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.
arXiv comment6 pages, 5 figures, accepted in Chaos: An Interdisciplinary Journal of Nonlinear Science
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- Transition from homogeneous to inhomogeneous steady states in oscillators under cyclic coupling
- Synchronization of wave structures in a heterogeneous multiplex network of 2D vdP lattices with attractive and repulsive intra-layer coupling
- Infection spreading and recovery in a square lattice
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- Emergent dynamics in delayed attractive-repulsively coupled networks
- Dynamics of coupled modified Rossler oscillators: the role of nonisochronicity parameter