Imperfect bifurcation of systems with slowly varying parameters and application to Duffing's equation |
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Authors: | Hua Cun-cai Lu Qi-shao |
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Institution: | (1) School of Science, Beijing University of Aeronautics and Astronautics, 100083 Beijing, P R China |
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Abstract: | A new method was proposed for essentially studying the imperfect bifurcation problem of nonlinear systems with a slowly varying parameter. By establishing some theorems on the solution approximated by that of the linearized system, the delayed bifurcation transition and jump phenomena of the time_dependent equation were analyzed. V_function was used to predict the bifurcation transition value. Applying the new method to analyze the Duffing's equation, some new results about bifurcation as well as that about the sensitivity of the solutions with respect to initial values and parameters are obtained. |
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Keywords: | time_dependent parametric system bifurcation transition imperfect bifurcation Duffing's equation |
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