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Higher-Order Network Interactions through Phase Reduction for Oscillators with Phase-Dependent Amplitude
- Source :
- Journal of Nonlinear Science, 34:77, 2024
- Publication Year :
- 2023
-
Abstract
- Coupled oscillator networks provide mathematical models for interacting periodic processes. If the coupling is weak, phase reduction -- the reduction of the dynamics onto an invariant torus -- captures the emergence of collective dynamical phenomena, such as synchronization. While a first-order approximation of the dynamics on the torus may be appropriate in some situations, higher-order phase reductions become necessary, for example, when the coupling strength increases. However, these are generally hard to compute and thus they have only been derived in special cases: This includes globally coupled Stuart--Landau oscillators, where the limit cycle of the uncoupled nonlinear oscillator is circular as the amplitude is independent of the phase. We go beyond this restriction and derive second-order phase reductions for coupled oscillators for arbitrary networks of coupled nonlinear oscillators with phase-dependent amplitude, a scenario more reminiscent of real-world oscillations. We analyze how the deformation of the limit cycle affects the stability of important dynamical states, such as full synchrony and splay states. By identifying higher-order phase interaction terms with hyperedges of a hypergraph, we obtain natural classes of coupled phase oscillator dynamics on hypergraphs that adequately capture the dynamics of coupled limit cycle oscillators.<br />Comment: 30 pages, 4 figures
Details
- Database :
- arXiv
- Journal :
- Journal of Nonlinear Science, 34:77, 2024
- Publication Type :
- Report
- Accession number :
- edsarx.2305.04277
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1007/s00332-024-10053-3