本文研究线性时滞反馈导致van der Pol-Duffing系统非共振双Hopf分岔分类、分岔解计算以及混沌运动。通过对线性化系统的分析,得到系统出现非共振双Hopf分岔以参数时滞和反馈增益表示的充分必要条件,在1:2双Hopf分岔点的邻域内,将系统...
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本文研究线性时滞反馈导致van der Pol-Duffing系统非共振双Hopf分岔分类、分岔解计算以及混沌运动。通过对线性化系统的分析,得到系统出现非共振双Hopf分岔以参数时滞和反馈增益表示的充分必要条件,在1:2双Hopf分岔点的邻域内,将系统约化四维中心流形并将其简化以物理参数表示的规范性,对分岔点的邻域内的分岔解进行了分类,得到分岔解的近似解析表达式,数值模拟从定性和定量两个方面验证分类和解析表达式的正确性,其中包括周期解和概周期解。对于远离了分岔点的值,由中心流形方法得到的解析表达式已经不能满足精度的要求,提出和构造的摄动增量法(PIS)可以有效的克服中心流形方法这一缺陷。本文的结果表明,系统在非共振双Hopf分岔点的邻域内有丰富的动力学现象,不但存在“振幅死区”和周期解,而且还存在着概周期解和混沌区。利用本文的结果,可以通过调节反馈时滞和增益,实现对系统的控制。
— In this paper we analyze the feedback stabi- lizability of Hopf bifurcations with SO(2) symmetry. The mode associated with the eigenvalues that become linearly unstable is assumed to be linearly uns
— In this paper we analyze the feedback stabi- lizability of Hopf bifurcations with SO(2) symmetry. The mode associated with the eigenvalues that become linearly unstable is assumed to be linearly uns
A two-dimensional (2D) mathematic model of the cross coupling Logistic mapping based on one-dimensional (1D) Logistic mapping is constructed , bifurcation structure of the 2D system is founded to be f
A two-dimensional (2D) mathematic model of the cross coupling Logistic mapping based on one-dimensional (1D) Logistic mapping is constructed , bifurcation structure of the 2D system is founded to be f
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