Study of differential control method for solving chaotic solutions of nonlinear dynamic system |
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Authors: | Email author" target="_blank">Li-guo?WangEmail author Xiangjun?Zhang Dianguo?Xu Wenhu?Huang |
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Institution: | 1.Dept. of Electrical Eng.,Harbin Institute of Technology,Harbin,China;2.Dept. of Aerospace Eng. and Mech.,Harbin Institute of Technology,Harbin,China |
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Abstract: | In this paper, we focus on the need to solve chaotic solutions of high-dimensional nonlinear dynamic systems of which the
analytic solution is difficult to obtain. For this purpose, a Differential Control Method (DCM) is proposed based on the Mechanized
Mathematics-Wu Elimination Method (WEM). By sampling, the computer time of the differential operator of the nonlinear differential
equation can be substituted by the differential quotient of solving the variable time of the sample. The main emphasis of
DCM is placed on substituting the differential quotient of a small neighborhood of the sample time of the computer system
for the differential operator of the equations studied. The approximate analytical chaotic solutions of the nonlinear differential
equations governing the high-dimensional dynamic system can be obtained by the method proposed. In order to increase the computational
efficiency of the method proposed, a thermodynamics modeling method is used to decouple the variable and reduce the dimension
of the system studied. The validity of the method proposed for obtaining approximate analytical chaotic solutions of the nonlinear
differential equations is illustrated by the example of a turbo-generator system. This work is applied to solving a type of
nonlinear system of which the dynamic behaviors can be described by nonlinear differential equations. |
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