ArticleIEEE transactions on automatic control2012
Exponential synchronization rate of Kuramoto oscillators in the presence of a pacemaker.
Article in IEEE transactions on automatic control, 2012. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 2 papers.
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2 citing papers in PubMed.
- Fixed-Time Synchronization of Coupled Oscillator Networks with a Pacemaker.Sensors (Basel, Switzerland) · 2022Article
- Models of communication and control for brain networks: distinctions, convergence, and future outlook.Network neuroscience (Cambridge, Mass.) · 2020Article
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Abstract
The exponential synchronization rate is addressed for Kuramoto oscillators in the presence of a pacemaker. When natural frequencies are identical, we prove that synchronization can be ensured even when the phases are not constrained in an open half-circle, which improves the existing results in the literature. We derive a lower bound on the exponential synchronization rate, which is proven to be an increasing function of pacemaker strength, but may be an increasing or decreasing function of local coupling strength. A similar conclusion is obtained for phase locking when the natural frequencies are non-identical. An approach to trapping phase differences in an arbitrary interval is also given, which ensures synchronization in the sense that synchronization error can be reduced to an arbitrary level.
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