多平衡态下簇发振荡产生机理及吸引子结构分析

发布时间：2018-04-20 12:42

本文选题：不同尺度耦合 + 多平衡态　；参考：《物理学报》2016年09期

【摘要】：以周期激励下受控Lorenz模型为例,考察了多平衡态共存下激励频率与系统固有频率之间存在量级差距也即存在频域上的不同尺度时的耦合效应.由于激励频率远小于系统的固有频率,因此将整个激励项视为慢变参数,分析随慢变参数变化下的各种分岔模式及其相应的分岔行为,指出在一定条件下,不同平衡点会产生Hopf分岔和fold分岔.根据分岔条件的不同,给出了两种典型情况下的簇发振荡,并通过引入转换相图,揭示了不同簇发的产生机理,指出多平衡态和多种分岔共存不仅会导致沉寂态和激发态的多样性,而且会使得不同沉寂态和激发态之间存在着不同的转换形式.
[Abstract]:Taking the controlled Lorenz model under periodic excitation as an example, the coupling effect is investigated when there is an order of magnitude difference between the excitation frequency and the natural frequency of the system under the coexistence of multi-equilibrium states, that is, the existence of different scales in frequency domain. Since the excitation frequency is far less than the natural frequency of the system, the whole excitation term is regarded as a slow-varying parameter. The bifurcation modes and their corresponding bifurcation behaviors with the variation of the slow-varying parameters are analyzed, and it is pointed out that under certain conditions, Hopf bifurcation and fold bifurcation will occur at different equilibrium points. According to the different bifurcation conditions, two typical cluster oscillations are given. By introducing the transformation phase diagram, the generation mechanism of different clusters is revealed. It is pointed out that the coexistence of multiple equilibrium states and multiple bifurcations will not only lead to the diversity of silent and excited states, but also lead to the existence of different transformation forms between different silent states and excited states.
【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(批准号:21276115,11472115,11472116)资助的课题~~
【分类号】：O641

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