Guaranteeing global synchronization in networks with stochastic interactions. (English) Zbl 1448.92031
Summary: We design the interactions between oscillators communicating via variably delayed pulse coupling to guarantee their synchronization on arbitrary network topologies. We identify a class of response functions and prove convergence to network-wide synchrony from arbitrary initial conditions. Synchrony is achieved if the pulse emission is unreliable or intentionally probabilistic. These results support the design of scalable, reliable and energy-efficient communication protocols for fully distributed synchronization as needed, e.g., in mobile phone networks, embedded systems, sensor networks and autonomously interacting swarm robots.
MSC:
| 92B25 | Biological rhythms and synchronization |
| 34D06 | Synchronization of solutions to ordinary differential equations |
| 34C15 | Nonlinear oscillations and coupled oscillators for ordinary differential equations |
| 90B15 | Stochastic network models in operations research |
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