Two-cluster bifurcations in systems of globally pulse-coupled oscillators
Please always quote using this URN:urn:nbn:de:0296-matheon-8225
- 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 phaseresponse- 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.
Author: | Leonhard Lücken, Serhiy Yanchuk |
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URN: | urn:nbn:de:0296-matheon-8225 |
Referee: | Alexander Mielke |
Document Type: | Preprint, Research Center Matheon |
Language: | English |
Date of first Publication: | 2011/04/29 |
Release Date: | 2011/04/29 |
Institute: | Humboldt-Universität zu Berlin |
MSC-Classification: | 34-XX ORDINARY DIFFERENTIAL EQUATIONS / 34Cxx Qualitative theory [See also 37-XX] / 34C15 Nonlinear oscillations, coupled oscillators |
37-XX DYNAMICAL SYSTEMS AND ERGODIC THEORY [See also 26A18, 28Dxx, 34Cxx, 34Dxx, 35Bxx, 46Lxx, 58Jxx, 70-XX] / 37Exx Low-dimensional dynamical systems / 37E05 Maps of the interval (piecewise continuous, continuous, smooth) | |
37-XX DYNAMICAL SYSTEMS AND ERGODIC THEORY [See also 26A18, 28Dxx, 34Cxx, 34Dxx, 35Bxx, 46Lxx, 58Jxx, 70-XX] / 37Gxx Local and nonlocal bifurcation theory [See also 34C23, 34K18] / 37G35 Attractors and their bifurcations | |
Preprint Number: | 787 |