Intrinsic Resonance depends on Network Size of Coupled-Delayed Interacting Oscillators
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| Format: | Preprint |
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2025
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| _version_ | 1866912937995665408 |
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| author | Torres, Felipe A. Weinstein, Alejandro Cortes, Jesus M. El-Deredy, Wael |
| author_facet | Torres, Felipe A. Weinstein, Alejandro Cortes, Jesus M. El-Deredy, Wael |
| contents | The collective frequency that emerges from synchronized neuronal populations--the network resonance--shows a systematic relationship with brain size: whole-brain's large networks oscillate slowly, whereas finer parcellations of fixed volume exhibit faster rhythms. This resonance-size scaling has been reported in delayed neural mass models and human neuroimaging, yet the physical mechanism remained unresolved. Here we show that size-dependent resonance follows directly from propagation delays in delay-coupled phase oscillators. Starting from a Kuramoto model with heterogeneous delays, we linearize around the near-synchronous solution and obtain a closed-form approximation linking the resonance $Ω$ to the mean delay and the effective coupling field. The analysis predicts a generic scaling law: $Ω\approx (\sum_j c_{ij} τ)^{-1}$, so resonance is delay-limited and therefore depends systematically on geometric size or parcellation density. We evaluate four growth scenarios--expanding geometry, fixed-volume parcellation, constant geometry, and an unphysical reference case--and show that only geometry-consistent scaling satisfies the analytical prediction. Numerical simulations with heterogeneous delays validate the law and quantify its error as a function of delay dispersion. These results identify a minimal physical mechanism for size-dependent cortical resonance and provide an analytical framework that unifies numeric simulation outputs. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_14065 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Intrinsic Resonance depends on Network Size of Coupled-Delayed Interacting Oscillators Torres, Felipe A. Weinstein, Alejandro Cortes, Jesus M. El-Deredy, Wael Neurons and Cognition Systems and Control The collective frequency that emerges from synchronized neuronal populations--the network resonance--shows a systematic relationship with brain size: whole-brain's large networks oscillate slowly, whereas finer parcellations of fixed volume exhibit faster rhythms. This resonance-size scaling has been reported in delayed neural mass models and human neuroimaging, yet the physical mechanism remained unresolved. Here we show that size-dependent resonance follows directly from propagation delays in delay-coupled phase oscillators. Starting from a Kuramoto model with heterogeneous delays, we linearize around the near-synchronous solution and obtain a closed-form approximation linking the resonance $Ω$ to the mean delay and the effective coupling field. The analysis predicts a generic scaling law: $Ω\approx (\sum_j c_{ij} τ)^{-1}$, so resonance is delay-limited and therefore depends systematically on geometric size or parcellation density. We evaluate four growth scenarios--expanding geometry, fixed-volume parcellation, constant geometry, and an unphysical reference case--and show that only geometry-consistent scaling satisfies the analytical prediction. Numerical simulations with heterogeneous delays validate the law and quantify its error as a function of delay dispersion. These results identify a minimal physical mechanism for size-dependent cortical resonance and provide an analytical framework that unifies numeric simulation outputs. |
| title | Intrinsic Resonance depends on Network Size of Coupled-Delayed Interacting Oscillators |
| topic | Neurons and Cognition Systems and Control |
| url | https://arxiv.org/abs/2511.14065 |