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Structurally Unstable Synchronization and Border-Collision Bifurcations in the Two-Coupled Izhikevich Neuron Model
https://tokushima-u.repo.nii.ac.jp/records/2011428
https://tokushima-u.repo.nii.ac.jp/records/20114286c269eb3-8c47-405d-aac5-84306b347c92
| 名前 / ファイル | ライセンス | アクション |
|---|---|---|
ijbc_33_16_2330040.pdf (1.54 MB)
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| Item type | 文献 / Documents(1) | |||||||||||||||||
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| 公開日 | 2024-02-08 | |||||||||||||||||
| アクセス権 | ||||||||||||||||||
| アクセス権 | open access | |||||||||||||||||
| アクセス権URI | http://purl.org/coar/access_right/c_abf2 | |||||||||||||||||
| 資源タイプ | ||||||||||||||||||
| 資源タイプ識別子 | http://purl.org/coar/resource_type/c_6501 | |||||||||||||||||
| 資源タイプ | journal article | |||||||||||||||||
| 出版社版DOI | ||||||||||||||||||
| 関連識別子 | https://doi.org/10.1142/S0218127423300409 | |||||||||||||||||
| 関連名称 | 10.1142/S0218127423300409 | |||||||||||||||||
| 出版タイプ | ||||||||||||||||||
| 出版タイプ | AM | |||||||||||||||||
| 出版タイプResource | http://purl.org/coar/version/c_ab4af688f83e57aa | |||||||||||||||||
| タイトル | ||||||||||||||||||
| タイトル | Structurally Unstable Synchronization and Border-Collision Bifurcations in the Two-Coupled Izhikevich Neuron Model | |||||||||||||||||
| 著者 |
美井野, 優
× 美井野, 優
× 上田, 哲史
WEKO
98
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| 抄録 | ||||||||||||||||||
| 内容記述 | This study investigates a structurally unstable synchronization phenomenon observed in the two-coupled Izhikevich neuron model. As the result of varying the system parameter in the region of parameter space close to where the unstable synchronization is observed, we find significant changes in the stability of its periodic motion. We derive a discrete-time dynamical system that is equivalent to the original model and reveal that the unstable synchronization in the continuous-time dynamical system is equivalent to border-collision bifurcations in the corresponding discrete-time system. Furthermore, we propose an objective function that can be used to obtain the parameter set at which the border-collision bifurcation occurs. The proposed objective function is numerically differentiable and can be solved using Newton’s method. We numerically generate a bifurcation diagram in the parameter plane, including the border-collision bifurcation sets. In the diagram, the border-collision bifurcation sets show a novel bifurcation structure that resembles the ‘strike-slip fault’ observed in geology. This structure implies that, before and after the border-collision bifurcation occurs, the stability of the periodic point discontinuously changes in some cases but maintains in other cases. In addition, we demonstrate that a border-collision bifurcation sets successively branch at distinct points. This behavior results in a tree-like structure being observed in the border-collision bifurcation diagram; we refer to this structure as a border-collision bifurcation tree. We observe that a periodic point disappears at the border-collision bifurcation in the discrete-time dynamical system and is simultaneously replaced by another periodic point; this phenomenon corresponds to a change in the firing order in the continuous-time dynamical system. | |||||||||||||||||
| キーワード | ||||||||||||||||||
| 主題 | two-coupled Izhikevich neuron model | |||||||||||||||||
| キーワード | ||||||||||||||||||
| 主題 | structurally unstable synchronization | |||||||||||||||||
| キーワード | ||||||||||||||||||
| 主題 | border-collision bifurcation | |||||||||||||||||
| 書誌情報 |
en : International Journal of Bifurcation and Chaos 巻 33, 号 16, p. 2330040, 発行日 2023-12-30 |
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| 収録物ID | ||||||||||||||||||
| 収録物識別子タイプ | ISSN | |||||||||||||||||
| 収録物識別子 | 02181274 | |||||||||||||||||
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| 収録物識別子タイプ | ISSN | |||||||||||||||||
| 収録物識別子 | 17936551 | |||||||||||||||||
| 収録物ID | ||||||||||||||||||
| 収録物識別子タイプ | NCID | |||||||||||||||||
| 収録物識別子 | AA10810319 | |||||||||||||||||
| 出版者 | ||||||||||||||||||
| 出版者 | World Scientific | |||||||||||||||||
| 権利情報 | ||||||||||||||||||
| 権利情報 | Electronic version of an article published as International Journal of Bifurcation and Chaos, Vol.33, No.16, 2023, 2330040, 10.1142/S0218127423300409 © World Scientific Publishing Company https://www.worldscientific.com/worldscinet/ijbc | |||||||||||||||||
| EID | ||||||||||||||||||
| 識別子 | 403709 | |||||||||||||||||
| 言語 | ||||||||||||||||||
| 言語 | eng | |||||||||||||||||
