Geometry unites synchrony, chimeras, and waves in nonlinear oscillator networks
Abstract
One of the simplest mathematical models in the study of nonlinear systems is the Kuramoto model, which describes synchronization in systems from swarms of insects to superconductors. We have recently found a connection between the original, real-valued nonlinear Kuramoto model and a corresponding complex-valued system that permits describing the system in terms of a linear operator and iterative update rule. We now use this description to investigate three major synchronization phenomena in Kuramoto networks (phase synchronization, chimera states, and traveling waves), not only in terms of steady state solutions but also in terms of transient dynamics and individual simulations. These results provide new mathematical insight into how sophisticated behaviors arise from connection patterns in nonlinear networked systems.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Mar 01, 2022
- Source ID
- 10.1063/5.0078791
Entities
People
- Jacqueline Đoàn
- Ján Mináč
- Lyle E. Muller
- Roberto Budzinski
- Terrence J. Sejnowski
- Tung T. Nguyen
Organizations
- Canada First Research Excellence Fund
- National Institutes of Health
- National Science Foundation
- Natural Sciences and Engineering Research Council
- Office of Naval Research
- Salk Institute for Biological Studies
- University of California, San Diego
- Western University