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    Formal Lagrangian Operad by Alberto S. Cattaneo, Benoit Dherin, Giovanni Felder

    Published 2010-01-01
    “…Given a symplectic manifold M, we may define an operad structure on the the spaces Ok of the Lagrangian submanifolds of (M¯)k×M via symplectic reduction. …”
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    Neimark-Sacker Bifurcation Analysis for a Discrete-Time System of Two Neurons by Changjin Xu

    Published 2012-01-01
    “…A formula determining the direction and stability of Neimark-Sacker bifurcation by applying normal form theory and center manifold theorem is given. Finally, some numerical simulations for justifying the theoretical results are also provided.…”
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    Stability and Hopf Bifurcation for a Delayed SLBRS Computer Virus Model by Zizhen Zhang, Huizhong Yang

    Published 2014-01-01
    “…Specially, direction and stability of the Hopf bifurcation are derived by applying the normal form method and center manifold theory. Finally, an illustrative example is also presented to testify our analytical results.…”
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    Multiplicity Results for p-Laplacian with Critical Nonlinearity of Concave-Convex Type and Sign-Changing Weight Functions by Tsing-San Hsu

    Published 2009-01-01
    “…The study is based on the extraction of Palais-Smale sequences in the Nehari manifold.…”
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    Derivation of Asymptotic Dynamical Systems with Partial Lie Symmetry Groups by Masatomo Iwasa

    Published 2015-01-01
    “…The main characteristic of the extended method is the restriction of the manifold by some constraint equations on which we search for a Lie symmetry group. …”
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    Stability and Hopf Bifurcation for a Delayed Computer Virus Model with Antidote in Vulnerable System by Zizhen Zhang, Yougang Wang, Massimiliano Ferrara

    Published 2017-01-01
    “…Further, direction of the Hopf bifurcation and stability of the bifurcating periodic solutions are investigated by using the normal form theory and the center manifold theorem. Finally, numerical simulations are presented to show consistency with the obtained results.…”
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    A neural network model for goat gait by Liqin Liu, Chunrui Zhang

    Published 2024-08-01
    “…First, we computed the normal form of the model on the center manifold, the bifurcation direction, and stability conditions of the bifurcating periodic solutions. …”
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