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首页> 外文会议>ASME(American Society of Mechanical Engineers) International Design Engineering Technical Conferences and Computers and Information in Engineering Conference 2005(DETC2005) vol.1: Biennial Conference on Mechanical Vibration and Noisen pt.A; 20050924-28; >AN EFFICIENT COMPUTATION METHOD FOR HOPF BIFURCATION OF HIGH DIMENSIONAL SYSTEMS
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AN EFFICIENT COMPUTATION METHOD FOR HOPF BIFURCATION OF HIGH DIMENSIONAL SYSTEMS

机译：高维系统Hopf分岔的一种有效计算方法。

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摘要

Normal form theory is a powerful tool in the study of nonlinear systems, in particular, for complex dynamical behaviors such as stability and bifurcations. However, it has not been widely used in practice due to the lack of efficient computation methods, especially for high dimensional engineering problems. The main difficulty in applying normal form theory is to determine the critical conditions under which the dynamical system undergoes a bifurcation. In this paper a computationally efficient method is presented for determining the critical condition of Hopf bifurcation by calculating the Jacobian matrix and the Hurwitz condition. This method combines numerical and symbolic computation schemes, and can be applied to high dimensional systems. The Lorenz system and the extended Malkus-Robbins dynamo system are used to show the applicability of the method.
机译：范式理论是研究非线性系统的有力工具，尤其是对于复杂的动力学行为（例如稳定性和分叉）而言。但是，由于缺乏有效的计算方法，尤其是对于高维工程问题，它尚未在实践中得到广泛使用。应用范式理论的主要困难是确定动力学系统发生分叉的临界条件。本文提出了一种计算有效的方法，通过计算雅可比矩阵和Hurwitz条件来确定Hopf分叉的临界条件。该方法结合了数值和符号计算方案，可应用于高维系统。使用Lorenz系统和扩展的Malkus-Robbins发电机系统来证明该方法的适用性。

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