NHÀ khoa học nguyễn văN ĐẠo với lý thuyết dao đỘng và chuyểN ĐỘng hỗN ĐỘN


Vietnamese Academy of Science and Technology



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Chuyển đổi dữ liệu15.11.2017
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Vietnamese Academy of Science and Technology




Abstract. In the present paper the influence of the excitation frequency () and the forcing amplitude (e) on the chaotic behaviour of the system governed by equation

(1)

will be examined. This equation is a Van der Pol one with a forcing term esinvt, where and are constants, overdot denotes the derivative with respect to time t .When e=0 , we have the classical Van der Pol equation which represents a self excited oscillator with the amplitude and frequency . Our discussion was focused upon variation of the excitation frequency and the forcing amplitude e . The bifurcation diagrams for acquiring the overview of equation (1) and the Liapunov exponent method will be used [3,4,5,6,9].

For a concrete case, the parameter regions in which either periodic or chaotic motions exist were shown. In two preceding cases, the first case, when is control parameter, it changes suddenly from periodic motion to chaotic motion, corresponding to Hopf bifurcation. In the second case, it is the double period process and leads to chaotic motion.Chaotic attractors illustrate the complexity of the motion of the system under consideration.



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