Abstract
The Kuramoto model describes the synchronization of a heterogeneous population of oscillators through a stationary homogeneous network in which oscillators are coupled via their phase differences. Recently, there has been interest in studying synchronization on time-varying networks, and time-varying generalizations of the Kuramoto network, in particular. Previous results indicate that networks with fast dynamics may be as efficient as static networks at promoting synchrony. In this paper we use optimal control theory to study synchronization on a time-varying Kuramoto network. Our results indicate that time-varying networks can be more efficient than static networks at promoting synchrony and show that fast network dynamics are not necessary for efficiency. In particular, we show that, near the synchronization threshold, time-varying networks can promote synchrony through slow oscillations that lengthen the duration of high synchrony states and shorten the duration of low synchrony states. Interestingly, repulsion is an essential feature of these optimal dynamic networks.
| Original language | English |
|---|---|
| Pages (from-to) | 36-47 |
| Number of pages | 12 |
| Journal | Physica D: Nonlinear Phenomena |
| Volume | 301-302 |
| DOIs | |
| State | Published - May 1 2015 |
Funding
The work of Lenhart and Leander was partially supported by the National Institute for Mathematical and Biological Synthesis, sponsored by the National Science Foundation , the US Department of Homeland Security , and the US Department of Agriculture through NSF Award EF-0832858 . Lenhart’s work receives additional support from The University of Tennessee . Lenhart is also partially supported by the University of Tennessee Center for Business and Economic Research . The Oak Ridge National Laboratory is managed by UT-Battelle, LLC for the US Department of Energy under contract DE-AC05-00OR22725 .
Keywords
- Kuramoto oscillators
- Synchrony
- Time-varying coupling