频域两尺度簇发振荡结构及其动力学机制

发布时间：2018-03-18 21:56

  本文选题：两时间尺度　切入点：点-点式簇发　出处：《河南科技大学学报(自然科学版)》2017年04期 　论文类型：期刊论文

【摘要】：以非自治杜芬-范德波尔振子为例,探讨了当外激励频率与系统固有频率之间存在量级差异,也即存在频域不同尺度时的快慢耦合效应。通过固定低频激励项,分析了快子系统的稳定性和分岔行为,得到了对应的两参数分岔集。将分岔集划分为5个区域,并分析了与各区域相关的簇发振荡模式。揭示了对称式折/折和对称式亚临界Hopf/亚临界Hopf等点-点式簇发的行为,以及对称式亚临界Hopf/极限环折和对称式延迟超临界Hopf/延迟超临界Hopf等点-圈式簇发的行为。研究结果表明:快子系统的多解和多分岔共存是诱发各种对称式簇发振荡模式的重要原因。
[Abstract]:Taking the nonautonomous Duffin-van der Bohr oscillator as an example, the order of magnitude difference between the external excitation frequency and the natural frequency of the system is discussed, that is, the fast-slow coupling effect with different scales in the frequency domain. The stability and bifurcation behavior of the fast subsystem are analyzed, and the corresponding two parameter bifurcation sets are obtained. The bifurcation set is divided into five regions. The cluster oscillation modes related to each region are analyzed, and the behavior of symmetric folded / folded and symmetric subcritical Hopf/ subcritical Hopf is revealed. The behavior of symmetrically subcritical Hopf/ limit cycles and symmetric delayed-supercritical Hopf/ delayed-supercritical Hopf cluster is also studied. The results show that the coexistence of multiple solutions and multiple bifurcations of fast subsystems induces all kinds of symmetric clusters. An important reason for oscillating mode.
【作者单位】： 江苏大学土木工程与力学学院;
【基金】：国家自然科学基金项目(11632008,11572141,11502091,11472115,11402226)
【分类号】：O32
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本文编号：1631470