Characterization of Holomorphic Bisectional Curvature of GCR-Lightlike Submanifolds by Sangeet Kumar, Rakesh Kumar, R. K. Nagaich

“…We obtain the expressions for sectional curvature, holomorphic sectional curvature, and holomorphic bisectional curvature of a GCR-lightlike submanifold of an indefinite Kaehler manifold. We discuss the boundedness of holomorphic sectional curvature of GCR-lightlike submanifolds of an indefinite complex space form. …”
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Hopf Bifurcation and Stability Analysis of a Congestion Control Model with Delay in Wireless Access Network by Wen-bo Zhao, Xiao-ke Sun, Huicheng Wang

“…Furthermore, the direction and stability of the bifurcating periodic solutions are derived by applying the normal form theory and the center manifold theorem. Finally, some examples and numerical simulations are presented to show the feasibility of the theoretical results.…”
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The Existence Result for a Class of p-Kirchhoff-Type Problem with a Multilinear Growth Nonlinearity by Jiangyan Yao, Wei Han

“…The quantitative deformation lemma and Non-Nehari manifold method are used in the paper to prove the main results. …”
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Skein modules of links in cylinders over surfaces by Jens Lieberum

“…We define the Conway skein module 𝒞 (M) of ordered based links in a 3-manifold M. This module gives rise to 𝒞 (M)-valued invariants of usual links in M. …”
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Stability and Bifurcation Analysis in a Class of Two-Neuron Networks with Resonant Bilinear Terms by Changjin Xu, Xiaofei He

“…Some explicit formulae for determining the stability and the direction of the Hopf bifurcation periodic solutions bifurcating from Hopf bifurcations are obtained by using the normal form theory and center manifold theory. Finally, numerical simulations supporting the theoretical analysis are carried out.…”
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Dynamic System Analysis of Investment in Both Production and R&D with Time Delay by Debao Gao

“…By using the normal form theory and the center manifold theory, the discriminant formula of periodic solution property of investment model is given. …”
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Local controllability does imply global controllability by Boscain, Ugo, Cannarsa, Daniele, Franceschi, Valentina, Sigalotti, Mario

“…We say that a control system is locally controllable if the attainable set from any state $x$ contains an open neighborhood of $x$, while it is controllable if the attainable set from any state is the entire state manifold. We show in this note that a control system satisfying local controllability is controllable. …”
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Analysis of the Dynamical Properties of Discrete Predator-Prey Systems with Fear Effects and Refuges by Wei Li, Chunrui Zhang, Mi Wang

“…The critical coefficients and properties of bifurcating periodic solutions for Flip and Hopf bifurcations are computed using the center manifold theorem and bifurcation theory. Additionally, numerical simulations are employed to illustrate the bifurcation phenomenon and chaos characteristics. …”
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Dynamic Analysis for a Kaldor–Kalecki Model of Business Cycle with Time Delay and Diffusion Effect by Wenjie Hu, Hua Zhao, Tao Dong

“…Moreover, the normal form of Hopf bifurcations is obtained by using the center manifold theorem and normal form theory of the partial differential equation, which can determine the bifurcation direction and the stability of the periodic solutions. …”
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The Time Delays’ Effects on the Qualitative Behavior of an Economic Growth Model by Carlo Bianca, Massimiliano Ferrara, Luca Guerrini

“…Moreover, the existence of a Hopf bifurcation is proved and, by using the normal form theory and center manifold argument, the explicit formulas which determine the stability, direction, and period of bifurcating periodic solutions are obtained. …”
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Direction and Stability of Hopf Bifurcation in a Delayed Solow Model with Labor Demand by Sanaa ElFadily, Abdelilah Kaddar, Khalid Najib

“…By using a second order approximation of the center manifold, we compute the first Lyapunov coefficient for Hopf bifurcation points and we show that the system under consideration can undergo a supercritical or subcritical Hopf bifurcation and the bifurcating periodic solution is stable or unstable in a neighborhood of some bifurcation points, depending on the choice of parameters.…”
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Analyzing College Students’ Reading Behavior by AI Techniques by Fangxia Zheng

“…By insert the artificial intelligence (AI) techniques, manifold intelligent technologies such as arrange learning and semantic web last to emerge. …”
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Postural Synergies and Their Development by Mark L. Latash, Vijaya Krishnamoorthy, John P. Scholz, Vladimir M. Zatsiorsky

“…This approach, the uncontrolled manifold (UCM) hypothesis, is based on an assumption that the central nervous system organizes covariation of elemental variables to stabilize important performance variables in a task-specific manner. …”
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A note on background independence in AdS3 string theory by Bob Knighton

“…We provide a simple path integral argument that the path integral localizes onto holomorphic covering maps from the worldsheet to the boundary. For closed manifolds M $$ \mathcal{M} $$ , the gravitational path integral is argued to be trivial. …”
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Local solvability of a constrainedgradient system of total variation by Yoshikazu Giga, Yohei Kashima, Noriaki Yamazaki

“…A 1-harmonic map flow equation, a gradient system of total variation where values of unknowns are constrained in a compact manifold in ℝN, is formulated by the use of subdifferentials of a singular energythe total variation. …”
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Plant Leaf Recognition through Local Discriminative Tangent Space Alignment by Chuanlei Zhang, Shanwen Zhang, Weidong Fang

“…Manifold learning based dimensionality reduction algorithms have been payed much attention in plant leaf recognition as the algorithms can select a subset of effective and efficient discriminative features in the leaf images. …”
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Global Hopf Bifurcation Analysis for an Avian Influenza Virus Propagation Model with Nonlinear Incidence Rate and Delay by Yanhui Zhai, Ying Xiong, Xiaona Ma, Haiyun Bai

“…An explicit algorithm for determining the direction of the Hopf bifurcations and stability of the bifurcation periodic solutions is derived by applying the normal form theory and center manifold theorem. What is more, the global existence of periodic solutions is established by using a global Hopf bifurcation result.…”
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Qualitative Analysis of the Discretization of a Continuous Fractional Order Prey-Predator Model with the Effects of Harvesting and Immigration in the Population by Md. Jasim Uddin, Sarker Md. Sohel Rana

“…We show analytically that a fractional order prey-predator model supports both a Neimark–Sacker (NS) bifurcation and a period-doubling (PD) bifurcation under specific parametric circumstances. Using the central manifold and bifurcation theory, we provide evidence for NS and PD bifurcations. …”
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Chaos and bifurcation analysis of tumor-immune controlled system with time delay by Danni Wang, Hongli Yang, Liangui Yang

“…The Flip bifurcation and Neimark–Sacker bifurcation of system are proved by the normal form method, central manifold theorem, and bifurcation theory. The Gram–Schmidt orthonormalization (GSO) method is used to interpret the attractor properties of uncontrolled and controlled systems, it is revealed that the attractors of controlled systems are smaller than those of uncontrolled systems, and the theoretical and numerical results are consistent. …”
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Mathematical Modeling, Analysis, and Optimal Control of Corruption Dynamics by Haileyesus Tessema Alemneh

“…From the analysis using center manifold theory, the model exhibits forward bifurcation. …”
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