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    Bifurcation of Nongeneric Homoclinic Orbit Accompanied by Pitchfork Bifurcation by Fengjie Geng, Song Li

    Published 2014-01-01
    “…., the orbit comes from the equilibrium along the unstable manifold instead of the center manifold) connecting a nonhyperbolic equilibrium is investigated, and the nonhyperbolic equilibrium undergoes a pitchfork bifurcation. …”
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    Riemannian Gradient Algorithm for the Numerical Solution of Linear Matrix Equations by Xiaomin Duan, Huafei Sun, Xinyu Zhao

    Published 2014-01-01
    “…A Riemannian gradient algorithm based on geometric structures of a manifold consisting of all positive definite matrices is proposed to calculate the numerical solution of the linear matrix equation Q=X+∑i=1mAiTXAi. …”
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    Burgers’ Equations in the Riemannian Geometry Associated with First-Order Differential Equations by Z. Ok Bayrakdar, T. Bayrakdar

    Published 2018-01-01
    “…We see that an integral manifold of any PDE defines intrinsically flat and totally geodesic submanifold.…”
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  10. 570

    Orthopoxvirus Genes That Mediate Disease Virulence and Host Tropism by Sergei N. Shchelkunov

    Published 2012-01-01
    “…When understanding the mechanisms used by viruses to overcome manifold defense systems of the animal organism, represented by molecular factors and cells of the immune system, we would not only comprehend better but also discover new patterns of organization and function of these most important reactions directed against infectious agents. …”
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    The Aronsson Equation, Lyapunov Functions, and Local Lipschitz Regularity of the Minimum Time Function by Pierpaolo Soravia

    Published 2019-01-01
    “…We discuss how C1-supersolutions of (AE) become special Lyapunov functions of symmetric control systems, and allow to find continuous feedbacks driving the system to a target in finite time, except on a singular manifold. A consequence is a simple proof that the corresponding minimum time function is locally Lipschitz continuous away from the singular manifold, despite classical results showing that it should only be Hölder continuous unless appropriate conditions hold. …”
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  17. 577

    Nonlinear Integral Sliding Mode Control for a Second Order Nonlinear System by Xie Zheng, Xie Jian, Du Wenzheng, Cheng Hongjie

    Published 2015-01-01
    “…The new control scheme is characterized by a nonlinear integral sliding manifold which inherits the desired properties of the integral sliding manifold, such as robustness to system external disturbance. …”
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  18. 578

    Stability and Bifurcation for a Delayed Diffusive Two-Zooplankton One-Phytoplankton Model with Two Different Functions by Xin-You Meng, Li Xiao

    Published 2021-01-01
    “…The explicit formulas to determine the properties of Hopf bifurcation are given by the method of the normal form theory and center manifold theorem for partial functional differential equations. …”
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