Subcritical Hopf Bifurcation in the Delay Equation Model for Machine Tool Vibrations
作者： Tamás Kalmár-Nagy , Gábor Stépán , Francis C Moon , None
关键词: Nonlinear system 、 Delay differential equation 、 Differential equation 、 Saddle-node bifurcation 、 Mathematics 、 Computation 、 Mathematical analysis 、 Reduction (mathematics) 、 Hopf bifurcation 、 Center manifold
摘要: We show the existence of a subcritical Hopf bifurcation in thedelay-differential equation model so-called regenerative machine toolvibration. The calculation is based on reduction infinite-dimensional problem to two-dimensional center manifold. Due specialalgebraic structure delayed terms nonlinear part equation,the computation results simple analytical formulas. Numerical simulationsgave excellent agreement with results.
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