Higher-Order Network Interactions through Phase Reduction for Oscillators with Phase-Dependent Amplitude
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2023
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866916345051873280 |
|---|---|
| author | Bick, Christian Böhle, Tobias Kuehn, Christian |
| author_facet | Bick, Christian Böhle, Tobias Kuehn, Christian |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_04277 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Higher-Order Network Interactions through Phase Reduction for Oscillators with Phase-Dependent Amplitude Bick, Christian Böhle, Tobias Kuehn, Christian Dynamical Systems Disordered Systems and Neural Networks Adaptation and Self-Organizing Systems 34C15, 37Nxx, 35F15 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. |
| title | Higher-Order Network Interactions through Phase Reduction for Oscillators with Phase-Dependent Amplitude |
| topic | Dynamical Systems Disordered Systems and Neural Networks Adaptation and Self-Organizing Systems 34C15, 37Nxx, 35F15 |
| url | https://arxiv.org/abs/2305.04277 |