基于低频周期参数扰动统一混沌系统的分岔分析

发布时间：2018-12-15 23:15

【摘要】：以低频周期参数扰动下的统一混沌系统为研究对象,应用动力学基础知识,讨论了系统的平衡点的分布及其稳定性,得到了周期扰动系统的静态分岔和Hopf分岔的条件。根据Melnikov方法,计算得到了系统的同宿轨道以及系统发生同宿轨道分岔的条件。为了验证理论研究结果的正确性,采用数值模拟的方法进行了验证,结果表明理论研究结果正确。研究结果可以看做是对周期激励的Lorenz类系统和Chen类系统的总结,可以有助于混沌系统在计算机应用领域的推广和应用。
[Abstract]:Taking the unified chaotic system with low frequency periodic parameter perturbation as the research object, the distribution and stability of the equilibrium point of the system are discussed by applying the basic knowledge of dynamics, and the conditions of static bifurcation and Hopf bifurcation of the system with periodic perturbation are obtained. According to the Melnikov method, the homoclinic orbit of the system and the conditions for the bifurcation of the homoclinic orbit are obtained. In order to verify the correctness of the theoretical results, the numerical simulation method is used to verify the validity of the theoretical results. The results can be seen as a summary of periodic excitation Lorenz class systems and Chen class systems, and can be helpful to the popularization and application of chaotic systems in computer applications.
【作者单位】：天津大学机械工程学院;
【基金】：国家自然科学基金资助项目(51479136) 天津市自然科学基金资助项目(13JCZDJC27100)
【分类号】：O415.5

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