Delayed feedback control of synchronization in weakly coupled oscillator networks

Abstract

We study control of synchronization in weakly coupled oscillator networks by using a phase reduction approach. Starting from a general class of limit cycle oscillators we derive a phase model, which shows that delayed feedback control changes effective coupling strengths and effective frequencies. We derive the analytical condition for critical control gain, where the phase dynamics of the oscillator becomes extremely sensitive to any perturbations. As a result the network can attain phase synchronization even if the natural interoscillatory couplings are small. In addition, we demonstrate that delayed feedback control can disrupt the coherent phase dynamic in synchronized networks. The validity of our results is illustrated on networks of diffusively coupled Stuart--Landau and FitzHugh--Nagumo models.

References in corpus (2)

• Time-delayed feedback in neurosystems
• Optimal synchronization of complex networks

Cited by in corpus (5)

• In-phase synchronization in complex oscillator networks by adaptive delayed feedback control
• Optimal coupling functions for fast and global synchronization of weakly coupled limit-cycle oscillators
• Designing two-dimensional limit-cycle oscillators with prescribed trajectories and phase-response characteristics
• Unstable delayed feedback control to change sign of coupling strength for weakly coupled limit cycle oscillators
• Phase reduction of reaction-diffusion systems with delay