Dynamics of a Delayed Model for the Transmission of Malicious Objects in Computer Network by Zizhen Zhang, Huizhong Yang

“…For further investigation, properties of the periodic solutions are studied by using the normal form method and center manifold theory. Finally, some numerical simulations are given to justify the theoretical results.…”
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Quantum Mechanics on a Curved Snyder Space by Salvatore Mignemi, Rina Štrajn

“…Its representations can be obtained starting from those of the Snyder algebra and exploiting the geometrical properties of the phase space that can be identified with a Grassmannian manifold. Both the position and momentum operators turn out to have a discrete spectrum.…”
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Formal Lagrangian Operad by Alberto S. Cattaneo, Benoit Dherin, Giovanni Felder

“…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

“…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

“…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

“…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

“…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

“…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

“…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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Fixed-Point Results Related to b-Intuitionistic Fuzzy Metric Space by Mohamed Altanji, Annamalai Santhi, Vediyappan Govindan, Shyam Sundar Santra, Samad Noeiaghdam

“…Subsequently, we simplify the proofs of manifold fixed-point theorems in the intuitionistic fuzzy b-metric spaces under the prominent contraction conditions. …”
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Complex Dynamics in Generalized Hénon Map by Meixiang Cai

“…The conditions of existence for fold bifurcation, flip bifurcation, and Hopf bifurcation are derived by using center manifold theorem and bifurcation theory and checked up by numerical simulations. …”
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Hopf Bifurcation Analysis for a Computer Virus Model with Two Delays by Zizhen Zhang, Huizhong Yang

“…Furthermore, explicit formulae for determining direction of the Hopf bifurcation and stability of the bifurcating periodic solutions are obtained by using the normal form method and center manifold theory. Finally, some numerical simulations are presented to support the theoretical results.…”
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Stability and Hopf bifurcation in a diffusivepredator-prey system incorporating a prey refuge by Xiaoyuan Chang, Junjie Wei

“…Employing the center manifold theoryand normal form method, an algorithm for determining theproperties of the Hopf bifurcation is derived. …”
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Hopf Bifurcation of a Delayed Ecoepidemic Model with Ratio-Dependent Transmission Rate by Wanjun Xia, Soumen Kundu, Sarit Maitra

“…Furthermore, properties of the Hopf bifurcation are investigated by using the normal form theory and the center manifold theorem. Finally, numerical simulations are carried out in order to validate our obtained theoretical results.…”
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Worst-Case Performance Optimization Beamformer with Embedded Array’s Active Pattern by Yuyue Luo, Jin Pan, J. Andrew Zhang, Shaode Huang

“…Simulation and measured results consistently demonstrate the robustness and effectiveness of the proposed method in dealing with array manifold mismatches.…”
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EXPERIENCE IN ORGANIZING PATRIOTIC EDUCATION AT CLASSICAL UNIVERSITY by Oleg N. Shirokov, Tatyana N. Ivanova, Rustem A. Idrisov, Dmitriy A. Yaltaev, Sergey N. Kodybaykin

“…Ulyanov. A combination of manifold forms and methods in this area of educational activity ensures its efficiency. …”
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Interaction of Parametric and Forced Vibrations in High Speed Rotor-Bearing-Systems by Bernhardt Weyh

“…The method of enlarged systems serves as a toolbox, where the central idea of the method and the structure of the enlarged system are in the same way derived as the complete homogeneous and the manifold of inhomogeneous solutions are discussed. …”
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Bifurcation of a Microelectromechanical Nonlinear Coupling System with Delay Feedback by Yanqiu Li, Wei Duan, Shujian Ma, Pengfei Li

“…Explicit algorithms for determining the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are derived, using the theories of normal form and center manifold.…”
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Hopf Bifurcation of a Differential-Algebraic Bioeconomic Model with Time Delay by Xiaojian Zhou, Xin Chen, Yongzhong Song

“…Using the theories of normal form and center manifold, we also give the explicit algorithm for determining the direction of the Hopf bifurcations and the stability of the bifurcating periodic solutions. …”
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Linearization from Complex Lie Point Transformations by Sajid Ali, M. Safdar, Asghar Qadir

“…We identify such a class by employing complex structure on the manifold that defines the geometry of differential equations. …”
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