# Browsing by Author "Hu, Qingwen"

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Item Estimates of Periods and Global Continua of Periodic Solutions for State-Dependent Delay Equations(2012-07-10) Hu, Qingwen; Wu, J.; Zou, X.Show more We study the global Hopf bifurcation of periodic solutions for one-parameter systems of state-dependent delay differential equations, and specifically we obtain a priori estimates of the periods in terms of certain values of the state-dependent delay along continua of periodic solutions in the Fuller space C(ℝ; ℝ N+1) × ℝ 2. We present an example of three-dimensional state-dependent delay differential equations to illustrate the general results. © 2012 Society for Industrial and Applied Mathematics.Show more Item A Maximal Element Theorem in FWC-Spaces and its Applications(Hindawi Publishing Corporation, 2014-03-20) Lu, Haishu; Hu, Qingwen; Miao, Yulin; Hu, QingwenShow more A maximal element theorem is proved in finite weakly convex spaces (FWC-spaces, in short) which have no linear, convex, and topological structure. Using the maximal element theorem, we develop new existence theorems of solutions to variational relation problem, generalized equilibrium problem, equilibrium problem with lower and upper bounds, and minimax problem in FWC-spaces. The results represented in this paper unify and extend some known results in the literature.Show more Item Stabilization in a State-Dependent Model of Turning Processes(SIAM, 2012-01-03) Hu, Qingwen; Krawcewicz, Wieslaw; Turi, Jànos; 0000 0001 1616 0605 (Krawcewicz, W); 0000 0000 4128 774X (Turi, J); 89645792 (Krawcewicz, W); 88656618 (Turi, J); Hu, Qingwen; Krawcewicz, Wieslaw; Turi, JànosShow more We consider a two-degree-of-freedom model for turning processes which involves a system of differential equations with state-dependent delay. Depending on process parameters (e.g., spindle speed, depth of cut) the cutting tool can exhibit unwanted vibrations, resulting in a nonsmooth surface of the workpiece. In this paper we propose a feedback law to stabilize the turning process for a large range of system parameters. The feedback law introduces a generic nonhyperbolic stationary point into the model, which generates the main technical challenge of this work. We establish the stability equivalence between the differential equations with state-dependent delay and a corresponding nonlinear system with the delay fixed at its stationary value. Then we show the stability of that nonlinear system with constant delay by computing its normal form. Finally, we obtain conditions on system parameters which guarantee the stability of the state-dependent delay model at the nonhyperbolic stationary point. ©2012 Society for Industrial and Applied Mathematics.Show more