基于低频周期参数扰动统一混沌系统的分岔分析

Bifurcation analysis of unified chaotic system with low frequency periodic parametric perturbation

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。

This paper selected the unified chaotic system with a periodic parametric perturbation as the study subject, and discussed the equilibrium distribution and their stabilities, and obtained the condition of the fold bifurcation and Hopf bifurcation by dynamical knowledge. This paper calculated the homoclinic orbits of the system, and gave the bifurcation condition of homoclinic orbits based on Melnikov method. Numerical simulations are done to demonstrate that the analytical result is appropriate. The study result can be considered as a summary of periodic parametric perturbated Lorenz family systems and Chen family systems, and benefit the further application in computer science.