Two-cluster bifurcations in systems of globally pulse-coupled oscillators

Abstract

For a system of globally pulse-coupled phase-oscillators, we derive conditions for stability of the completely synchronous state and all possible two-cluster states and explain how the different states are naturally connected via bifurcations. The coupling is modeled using the phase-response-curve (PRC), which measures the sensitivity of each oscillator's phase to perturbations. For large systems with a PRC, which turns to zero at the spiking threshold, we are able to find the parameter regions where multiple stable two-cluster states coexist and illustrate this by an example. In addition, we explain how a locally unstable one-cluster state may form an attractor together will its homoclinic connections. This leads to the phenomenon of intermittent, asymptotic synchronization with abating beats away from the perfect synchrony.

12 pages. 6 figures

References in corpus (4)

• Zero-lag long-range synchronization via dynamical relaying
• Public Channel Cryptography: Chaos Synchronization and Hilbert's Tenth Problem
• Dynamics on Complex Networks and Applications
• Designing Complex Networks

Cited by in corpus (9)

• Multi-clusters in networks of adaptively coupled phase oscillators networks
• Synchronization Patterns: From Network Motifs to Hierarchical Networks
• Multistable jittering in oscillators with pulsatile delayed feedback
• Synchronization of Pulse-Coupled Oscillators and Clocks under Minimal Connectivity Assumptions
• Global Synchronization of Pulse-Coupled Oscillator Networks Under Byzantine Attacks
• Phase response function for oscillators with strong forcing or coupling
• Emergence and combinatorial accumulation of jittering regimes in spiking oscillators with delayed feedback
• Extreme multistability in symmetrically coupled clocks
• An Attack-Resilient Pulse-Based Synchronization Strategy for General Connected Topologies