n:m Phase-Locking of Coupled Oscillators with Nonlinearities in Coupling Strength and Heterogeneity
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910194650316800 |
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| author | Park, Youngmin |
| author_facet | Park, Youngmin |
| contents | We introduce a scalar reduction method for forced or coupled systems with nonlinearities in both heterogeneity and coupling strength. Heterogeneity is formulated as a relatively weak but nonlinear alteration of the vector field(s). The method can be used to determine the existence and stability of $n{:}m$ phase-locked states in a variety of forced or coupled biological oscillator models, including the nonradial isochron clock, a thalamic neural oscillator, and the Van der Pol oscillator. The proposed scalar reduction successfully captures the emergence and disappearance of phase-locked states as a function of nonlinear coupling strength and nonlinear heterogeneity. We find that even small amounts of heterogeneity can significantly alter phase-locked states in ways that cannot be captured by assuming identical oscillators. The proposed method enables a reduction and analysis of high-dimensional systems of coupled oscillators in more biologically realistic settings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_14566 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | n:m Phase-Locking of Coupled Oscillators with Nonlinearities in Coupling Strength and Heterogeneity Park, Youngmin Neurons and Cognition 92B25 We introduce a scalar reduction method for forced or coupled systems with nonlinearities in both heterogeneity and coupling strength. Heterogeneity is formulated as a relatively weak but nonlinear alteration of the vector field(s). The method can be used to determine the existence and stability of $n{:}m$ phase-locked states in a variety of forced or coupled biological oscillator models, including the nonradial isochron clock, a thalamic neural oscillator, and the Van der Pol oscillator. The proposed scalar reduction successfully captures the emergence and disappearance of phase-locked states as a function of nonlinear coupling strength and nonlinear heterogeneity. We find that even small amounts of heterogeneity can significantly alter phase-locked states in ways that cannot be captured by assuming identical oscillators. The proposed method enables a reduction and analysis of high-dimensional systems of coupled oscillators in more biologically realistic settings. |
| title | n:m Phase-Locking of Coupled Oscillators with Nonlinearities in Coupling Strength and Heterogeneity |
| topic | Neurons and Cognition 92B25 |
| url | https://arxiv.org/abs/2409.14566 |