期刊
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
卷 58, 期 4, 页码 989-994出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TAC.2012.2215772
关键词
Exponential synchronization rate; Kuramoto model; oscillator networks; pacemaker
资金
- U.S. ARO [W911NF-07-1-0279]
- NIH [GM078993]
- ICB from the U.S. ARO [W911NF-09-0001]
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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