摘要
针对Brussel模型的非线性方程,求解了系统的平衡点,理论推导了系统的稳定性,通过数值仿真的形式,揭示了系统随自身参数ω、A、B、a变化的动力学行为。用相图、时间历程图、全局分岔图揭示了系统随自身参数变化时的周期运动、多周期运动和混沌现象,分析了系统发生的倍化分岔行为和由倍化分岔序列通往混沌的现象,及随着参数的继续增大或减小,系统存在由混沌转变为周期运动、再由倍化分岔转变为多周期运动,最终通过倍化分岔序列通向混沌的往复行为,对比了系统随自身参数变化时的动力学行为的异同。从而全面揭示了Brussel系统随自身参数变化的复杂而丰富的动力学行为,为深化该模型在实际工程中的应用提供了理论依据,为探索该模型更丰富的动力学行为及混沌控制奠定了理论基础,同时为研究其它系统的动力学行为提供了方法和依据。
In the paper,solving the equilibrium point of the system that based on the nonlinear equation of the Brussel model,deriving the stability of the system,revealing the dynamic behavior of the system with its own parameters such as ω、A、B、a though of the numerical simulation. Revealing the periodic motion,multi periodic motion and chaos phenomenon of the system with its own parameters by used of the phase diagram,the time history diagram and the global bifurcation diagram,analyzing the behavior of the double bifurcation in the system and the phenomenon of the double bifurcation leading to chaos and with the increase or decrease of the parameters,the system is changed from chaos to periodic motion,and then transformed into multi periodic motion by the doubling bifurcation,the cyclic behavior of the chaotic system is eventually led to chaos finally,comparing the differences and similarities of the dynamic behaviors of the system with the system parameters. So revealing fully the complex and dynamic behaviors of the Brussel system with the changes of their parameters,it provides a theoretical basis in order to deepen the application of this model in practical engineering,and establish the theory foundation in order to explore the dynamic behavior and chaos control of the model,at the same time provide the method and basis for studying the dynamic behavior of other systems.
出处
《自动化与仪器仪表》
2016年第7期73-75,共3页
Automation & Instrumentation
基金
兰州石化职业技术学院教育教学研究课题项目(JY2014-26)
兰州石化职业技术学院科技教研项目(KJ2015-12)
