We study a network of three populations of coupled phase oscillators with identical frequencies. The populations interact nonlocally, in the sense that all oscillators are coupled to one another, but more weakly to those in neighboring populations than to those in their own population. Using this system as a model system, we discuss for the first time the influence of network topology on the existence of so-called chimera states. In this context, the network with three populations represents an interesting case because the populations may either be connected as a triangle, or as a chain, thereby representing the simplest discrete network of either a ring or a line segment of oscillator populations. We introduce a special parameter that allows us to study the effect of breaking the triangular network structure, and to vary the network symmetry continuously such that it becomes more and more chain-like. By showing that chimera states only exist for a bounded set of parameter values, we demonstrate that their existence depends strongly on the underlying network structures, and conclude that chimeras exist on networks with a chain-like character.
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December 2010
Research Article|
November 24 2010
Chimeras in a network of three oscillator populations with varying network topology
Erik A. Martens
Erik A. Martens
a)
Max Planck Research Group for Biological Physics and Evolutionary Dynamics,
Max Planck Institute for Dynamics and Self-Organization
, Göttingen 37073, Germany
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a)
Electronic mail: erik.martens@ds.mpg.de.
Chaos 20, 043122 (2010)
Article history
Received:
May 24 2010
Accepted:
September 21 2010
Citation
Erik A. Martens; Chimeras in a network of three oscillator populations with varying network topology. Chaos 1 December 2010; 20 (4): 043122. https://doi.org/10.1063/1.3499502
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