Hu, Qingwen

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Dr. Hu is interested in dynamical systems; state-dependent delay differential equations and their applications in engineering and biology; equivariant degree theory and applications; nonlinear analysis; and operations research.


Recent Submissions

Now showing 1 - 4 of 4
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    A Maximal Element Theorem in FWC-Spaces and its Applications
    (Hindawi Publishing Corporation, 2014-03-20) Lu, Haishu; Hu, Qingwen; Miao, Yulin; Hu, Qingwen
    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.
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    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, Jànos
    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.
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    Estimates of Periods and Global Continua of Periodic Solutions for State-Dependent Delay Equations
    (2012-07-10) Hu, Qingwen; Wu, J.; Zou, X.
    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.
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    Global Stability Lobes of Turning Processes with State-Dependent Delay
    (SIAM, 2012-09-13) 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, Jànos
    We obtain global stability lobes of two models of turning processes with inherit nonsmoothness due to the presence of state-dependent delays. In the process, we transform the models with state-dependent delays into systems of differential equations with both discrete and distributed delays and develop a procedure to determine analytically the global stability regions with respect to parameters. We find that the spindle speed control strategy that we investigated in [SIAM J. Appl. Math., 72 (2012), pp. 1–24] can provide essential improvement on the stability of turning processes with state-dependent delay, and furthermore we show the existence of a proper subset of the stability region which is independent of system damping. Numerical simulations are presented to illustrate the general results..

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