Spike-Adding Mechanisms in a Three-Timescale System: Insights from the FitzHugh-Nagumo Model with Periodic Forcing
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866912396609585152 |
|---|---|
| author | Melland, Pake Curtu, Rodica Aminzare, Zahra |
| author_facet | Melland, Pake Curtu, Rodica Aminzare, Zahra |
| contents | In this work, we investigate the spike-adding mechanism in a class of three-dimensional fast-slow systems with three distinct timescales, inspired by the FitzHugh-Nagumo (FHN) model driven by periodic input. First, we numerically generate a spike-adding diagram for the FHN model by varying the frequency and amplitude of the input, revealing that as the frequency decreases and the amplitude increases, the number of spikes within each burst grows. We demonstrate that a similar spike-adding structure occurs in the more realistic, periodically forced Morris-Lecar neuronal model. Next, we apply methods from geometric singular perturbation theory to compute critical and super-critical manifolds of the fast-slow system. We use them to characterize the emergence of new burst-spikes in the FHN model, when the periodic forcing resembles a low frequency-band brain rhythm. We then describe how the uncovered spike-adding mechanism defines the boundaries that separate regions with different spike counts in the parameter space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_00152 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Spike-Adding Mechanisms in a Three-Timescale System: Insights from the FitzHugh-Nagumo Model with Periodic Forcing Melland, Pake Curtu, Rodica Aminzare, Zahra Dynamical Systems Neurons and Cognition 34C23, 34C25, 34E13, 34D15, 92B05, 37N25 In this work, we investigate the spike-adding mechanism in a class of three-dimensional fast-slow systems with three distinct timescales, inspired by the FitzHugh-Nagumo (FHN) model driven by periodic input. First, we numerically generate a spike-adding diagram for the FHN model by varying the frequency and amplitude of the input, revealing that as the frequency decreases and the amplitude increases, the number of spikes within each burst grows. We demonstrate that a similar spike-adding structure occurs in the more realistic, periodically forced Morris-Lecar neuronal model. Next, we apply methods from geometric singular perturbation theory to compute critical and super-critical manifolds of the fast-slow system. We use them to characterize the emergence of new burst-spikes in the FHN model, when the periodic forcing resembles a low frequency-band brain rhythm. We then describe how the uncovered spike-adding mechanism defines the boundaries that separate regions with different spike counts in the parameter space. |
| title | Spike-Adding Mechanisms in a Three-Timescale System: Insights from the FitzHugh-Nagumo Model with Periodic Forcing |
| topic | Dynamical Systems Neurons and Cognition 34C23, 34C25, 34E13, 34D15, 92B05, 37N25 |
| url | https://arxiv.org/abs/2411.00152 |