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在可两位式的Duffing振荡器的参数空间中的碎形图案

Md Nahid Hasan¹, Taylor E Greenwood¹, Robert G Parker¹

¹Department of Mechanical Engineering, University of Utah, Salt Lake City, Utah 84112, USA.

Physical review. E

|September 19, 2023

概括

研究人员在一个消散式可视化Duffing振荡器的参数空间中发现了碎形模式. 这些发现揭示了对复杂系统动态的新见解,并指导了超材料设计.

科学领域:

非线性动力学是一种非线性动力学.
混沌理论混沌理论
机械超材料机械超材料

背景情况:

在非线性动力学中,Duffing振荡器是基本的.
碎形模式在相位空间中得到了很好的记录,但在参数空间中没有那么多.
了解参数空间复杂性对于系统控制和设计至关重要.

研究的目的:

为了研究散散式可比式Duffing振荡器的参数空间中的分数模式,具有相同的能量井.
量化区分不同振荡器行为边界的分数维度.
探讨对连续双位稳定系统和机械超材料设计的影响.

主要方法:

消散式可视化杜芬振荡器的数值模拟.
参数空间的分析 (驱动频率,强迫幅度,阻尼比率).
为已识别的边界计算豪斯多夫分形维度.

主要成果:

在参数空间中观察到碎形图案.
量化了洞内和洞间行为之间的边界的豪斯多夫分形维度.
将间隔行为分类为切换,反转和波动的稳定状态.
在连续双相系统的单模近似中确认了碎形模式.

结论:

碎形模式存在于可二位振荡器的参数空间中,提供了一个新的研究途径.
这项研究为理解和预测这些系统中的复杂行为提供了一个框架.
这些发现可以为先进的双稳定和多稳定机械超材料的设计提供信息.

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