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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Communicated by LI Jia-chun
Foundation item: the National Natural Science Foundation of China (19872010); the Aviation Science Foundation (98B51125); the Doctoral Program Foundation of the Education Committee of China (98000619)
Biography: HUA Cun-cai (1964≈)
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Cun-cai, H., Qi-shao, L. Imperfect bifurcation of systems with slowly varying parameters and application to Duffing's equation. Appl Math Mech 21, 1024–1033 (2000). https://doi.org/10.1007/BF02459312
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DOI: https://doi.org/10.1007/BF02459312