Abstract
Network structures are known to influence a population's propensity to synchronize. Previous attempts to identify synchrony promoting structures have focused on homogeneous populations. We use optimal control theory to construct networks that allow heterogeneous populations to maintain high levels of synchrony, explore the relationship between population heterogeneity and the structure of the optimal networks, and identify salient optimal network features that may enhance synchrony. In particular, we identify a new parameter, the average strength of neighbors, that may foster synchrony and observe that repulsion, in addition to attraction, can foster synchrony.
Original language | English |
---|---|
Pages (from-to) | 574-582 |
Number of pages | 9 |
Journal | Physica D: Nonlinear Phenomena |
Volume | 241 |
Issue number | 5 |
DOIs | |
State | Published - Mar 1 2012 |
Funding
The authors would like to thank Louis Gross for helpful suggestions. The work of Leander was partially supported by the National Science Foundation under Agreement No. 0931642 and partially supported by funding from the National Institute for Mathematical and Biological Synthesis on grant NSF EF-0832858 . The work of Lenhart was partially supported by funding from the National Institute for Mathematical and Biological Synthesis on grant NSF EF-0832858 . 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
- Optimal control
- Synchrony