シンメトリブレイクとタイムデレイドカップリング下での相振動器の動態
I Gowthaman1,2, M Manoranjani3,4, D V Senthilkumar5
1Institute of Systems Science and College of Information Science and Engineering, Huaqiao University, Xiamen 361021, China.
Physical review. E
|February 20, 2026
まとめ
この研究では,対称性破裂と時間遅延を持つ一般化されたKuramotoモデルを探求し,三つの異なるダイナミクスを明らかにします:不相干,静止同期,および静止波状態. 時間の遅延は,マルチスタビリティを導入し,カップリングされた振動器システムの同期パターンに影響を与えます.
科学分野:
- 複雑なシステム 複雑なシステム
- 非線形ダイナミクス 非線形ダイナミクス
- 理論物理学の理論物理学
背景:
- クラモトモデルは,カップリングされた振動器系における同期を研究するための基本的なツールです.
- 非対称性と時間遅延の影響を理解することは,現実的なモデリングに不可欠です.
研究 の 目的:
- シンメトリを破る相互作用と時間遅延を組み込んだ一般化されたKuramotoモデルを調査する.
- これらの改変から生じる新しい動的振る舞いを特定し,特徴づけること.
主な方法:
- シンメトリー破壊と時間遅延の相互作用を持つ一般化されたカップルされたKuramotoモデルの分析.
- オット・アントンセン・アンサツを応用して,複雑な順序パラメータの低次元方程式を導出する.
- 動的移行のためのバイフォーケーション曲線 (ホフ,ピッチフォーク,サドルノード) の決定.
主要な成果:
- モデルは3つの異なる動的状態を示しています:不相干,静止同期,および静止波.
- 対称性を破る相互作用の時間の遅延により,3つの多安定性領域が生じる.
- 静止同期状態の安定性は,時間遅延の相互作用に強固である.
結論:
- この一般化されたKuramotoモデルでは,対称性を破る相互作用の時間の遅延が,出現するビスタビリティに不可欠である.
- 順序パラメータ方程式から派生した分析予測は,数値シミュレーションとよく一致します.
- この研究は,遅延動的システムにおける複雑な同期現象の洞察を提供します.
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