Augmented phase reduction for periodic orbits near a homoclinic bifurcation and for relaxation oscillators
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- Monga Bharat
- Department of Mechanical Engineering, Engineering II Building, University of California Santa Barbara
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- Moehlis Jeff
- Department of Mechanical Engineering, Engineering II Building, University of California Santa Barbara
抄録
<p>Oscillators - dynamical systems with stable periodic orbits - arise in many systems of physical, technological, and biological interest. The standard phase reduction, a model reduction technique based on isochrons, can be unsuitable for oscillators which have a small-magnitude negative nontrivial Floquet exponent. This necessitates the use of the augmented phase reduction, a recently devised two-dimensional reduction technique based on isochrons and isostables. In this article, we calculate analytical expressions for the augmented phase reduction for two dynamically different planar systems: periodic orbits born out of homoclinic bifurcation, and relaxation oscillators. To validate our calculations, we simulate models in these dynamic regimes, and compare their numerically computed augmented phase reduction with the derived analytical expressions. These analytical and numerical calculations help us to understand conditions for which the use of augmented phase reduction over the standard phase reduction can be advantageous.</p>
収録刊行物
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- Nonlinear Theory and Its Applications, IEICE
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Nonlinear Theory and Its Applications, IEICE 12 (1), 103-116, 2021
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詳細情報 詳細情報について
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- CRID
- 1390568456341906304
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- NII論文ID
- 130007965491
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- ISSN
- 21854106
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- 本文言語コード
- en
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- データソース種別
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- JaLC
- Crossref
- CiNii Articles
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- 抄録ライセンスフラグ
- 使用不可