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混合模式振荡和极端事件在分数顺序的邦霍弗-范德波尔振荡器中
Zhouchao Wei1,2, Suresh Kumarasamy3, Mohanasubha Ramasamy3,4
1School of Mathematics and Physics, China University of Geosciences, Wuhan 430074, China.
Chaos (Woodbury, N.Y.)
|September 25, 2023
概括
分数顺序的邦霍弗-范德波尔 (BVP) 振荡器动态显示,较低的分数顺序消除了混合模式振荡 (MMO). 更高的分数订单表现出复杂的MMOs和危机,展示了丰富的BVP振荡器行为.
科学领域:
- 非线性动力学是一种非线性动力学.
- 分数微积分的计算.
- 振荡器系统 振荡器系统
背景情况:
- 众所周知,整数顺序的邦霍弗-范德波尔 (BVP) 振荡器在外部强迫下表现出混合模式振荡 (MMOs).
- 了解系统参数对振荡行为的影响在非线性动力学中至关重要.
研究的目的:
- 为了研究分数顺序的邦霍弗-范德波尔 (BVP) 振荡器的动态行为.
- 探索分数顺序对MMOs的发生和特征的影响.
- 在分数级BVP系统中识别新的动态现象,如危机.
主要方法:
- 使用数值模拟来分析分数级BVP振荡器.
- 外部强迫的频率被系统地改变,以观察振荡模式的变化.
- 研究了不同的分数顺序 (q1和q2),以评估它们对系统动态的影响.
主要成果:
- 分数顺序q1导致MMO振幅随着强迫频率的增加而减少,最终导致它们在较低的顺序上完全消失.
- 分数顺序q2导致了更复杂的MMOs,消除发生在更接近整数顺序的地方.
- 观察到一个危机现象,其特点是吸引力扩张和极端事件,因为分数顺序q2是变化的.
结论:
- 分数顺序显著影响BVP振荡器中的MMOs的存在和复杂性.
- 较低的分数订单可以抑制MMOs,而特定的分数订单可以诱导复杂的动态和危机.
- 分数级BVP振荡器表现出比其整数级对应器更丰富的动态谱.
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