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  1. 801
  2. 802

    On the Computation of Degenerate Hopf Bifurcations for n-Dimensional Multiparameter Vector Fields by Michail P. Markakis, Panagiotis S. Douris

    Published 2016-01-01
    “…The restriction of an n-dimensional nonlinear parametric system on the center manifold is treated via a new proper symbolic form and analytical expressions of the involved quantities are obtained as functions of the parameters by lengthy algebraic manipulations combined with computer assisted calculations. …”
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  3. 803

    Vector fields generating more than one flow by Slawomir Dorosiewicz, Kazimierz Napiórkowski

    Published 1995-01-01
    “…Vector fields generating more than one flow on a manifold are constructed. For one-dimensional case a complete description of the set of flows is given. …”
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  4. 804

    Stability and Local Hopf Bifurcation for a Predator-Prey Model with Delay by Yakui Xue, Xiaoqing Wang

    Published 2012-01-01
    “…Using the normal form theory and center manifold argument, the explicit formulae which determine the stability, direction, and other properties of bifurcating periodic solutions are derived.…”
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  5. 805
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    Bifurcation Analysis in a Kind of Fourth-Order Delay Differential Equation by Xiaoqian Cui, Junjie Wei

    Published 2009-01-01
    “…Then the direction and stability of the Hopf bifurcation are determined, using the normal form method and the center manifold theorem. Finally, some numerical simulations are carried out to illustrate the analytic results.…”
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  7. 807
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    Screen conformal half-lightlike submanifolds by K. L. Duggal, B. Sahin

    Published 2004-01-01
    “…We study some properties of a half-lightlike submanifold M, of a semi-Riemannian manifold, whose shape operator is conformal to the shape operator of its screen distribution. …”
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    Stability and bifurcation of numerical discretization Nicholson blowflies equation with delay by Xiaohua Ding, Wenxue Li

    Published 2006-01-01
    “…Applying the theory of normal form and center manifold, we not only discuss the linear stability of the equilibrium and the existence of the local Hopf bifurcations, but also give the explicit algorithm for determining the direction of bifurcation and stability of the periodic solution of bifurcation.…”
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  17. 817

    Hopf Bifurcation and Chaos of a Delayed Finance System by Xuebing Zhang, Honglan Zhu

    Published 2019-01-01
    “…Furthermore, formulas for determining the direction of Hopf bifurcation and the stability of the bifurcating periodic solutions are derived by applying the normal form method and center manifold theorem. Finally, numerical simulation results are presented to validate the theoretical analysis. …”
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  18. 818

    Stability and Hopf Bifurcation in a Diffusive Predator-Prey System with Beddington-DeAngelis Functional Response and Time Delay by Yuzhen Bai, Xiaopeng Zhang

    Published 2011-01-01
    “…Finally, the direction and stability of Hopf bifurcations are determined by normal form theory and center manifold reduction for partial functional differential equations.…”
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  19. 819

    The Bifurcation of Two Invariant Closed Curves in a Discrete Model by Yingying Zhang, Yicang Zhou

    Published 2018-01-01
    “…The conditions for existence of these bifurcations are derived by using the center manifold and bifurcation theory. Numerical simulations and bifurcation diagrams exhibit the complex dynamical behaviors, especially the occurrence of two invariant closed curves.…”
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