2012/09/04 by Yongqiang Wang, Francis J. Doyle, Wang, Yongqiang +1 · 1 citation
Computer Science · Engineering · Neuroscience · #Adaptation and Self-Organizing Systems (nlin.AO) #FOS: Electrical engineering #FOS: Physical sciences #Neural dynamics and brain function #Nonlinear Dynamics and Pattern Formation #Slime Mold and Myxomycetes Research #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.1209.0811
openalex publication_date 2012/09/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.