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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A weighted sparse constraint Capon beamforming algorithm by Yongxin DU, Xin MA, Baoshan LI, Ling QIN

“…Aiming at the problem of high sidelobes and nulls was not deep of Capon beamformer,the methods of reducing sidelobes and nulls were studied,a weighted sparse constraint Capon beamforming algorithm was proposed.Firstly,using the correlation operation of sidelobe array manifold matrix and the covariance matrix obtained the interference and noise energy were roughly posterior distribution in different directions.Then,different values were weighted in different directions according to the results,and restrained the interference.Simulation results show that the approach can reduce the sidelobes and deepen the null to fall the depth of the beam pattern,and improve the ability of suppress noise and interference.The proposed method is robust to both expected and array errors.…”
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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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Analysis of the effects of the amplitude-phase errors on spatial spectrum and resolving performance of the MUSIC algorithm by WANG Ding, WANG Chao, WU Ying

“…Compared to currently existing method,the first-order statistical expression of spatial spectrum only involves array manifold vector and source covariance matrix instead of the eigenvalue and eigenvector of the ideal array covariance matrix,besides,the mean SNR resolving threshold is suitable in the presence of power difference of two signal sources. …”
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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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Research on Constraint Violation Elimination based on Projection Method by Jia Liu, Yaru Xu, Kai Yang, Hongqiang Sun

“…In this method，the numerical solutions of the zero-order and first-order generalized variables of the system are projected to the constrained manifold defined by the constraint equation， the offsets of the numerical solution are obtained， then the offsets are transformed into the constraint force and integrated into Udwadia-Kalaba equation to achieve the purpose of restraining the constraint violation. …”
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Chaos and Hopf Bifurcation Analysis of the Delayed Local Lengyel-Epstein System by Qingsong Liu, Yiping Lin, Jingnan Cao, Jinde Cao

“…Moreover, we derive the equation describing the flow on the center manifold; then we give the formula for determining the direction of the Hopf bifurcation and the stability of bifurcating periodic solutions. …”
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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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Special Kähler geometry and holomorphic Lagrangian fibrations by Li, Yang, Tosatti, Valentino

“…Given a holomorphic Lagrangian fibration of a compact hyperkähler manifold, we use the differential geometry of the special Kähler metric that exists on the base away from the discriminant locus, and show that the pullback of the tangent bundle of the base to the total space of a family of minimal rational curves admits a parallel splitting. …”
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Duality by reproducing kernels by A. Shlapunov, N. Tarkhanov

“…Let A be a determined or overdetermined elliptic differential operator on a smooth compact manifold X. Write 𝒮A(𝒟) for the space of solutions of the system Au=0 in a domain 𝒟⋐X. …”
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