Stability and Hopf Bifurcation Analysis of a Vector-Borne Disease with Time Delay by Yuanyuan Chen, Ya-Qing Bi

“…The stability and direction of Hopf bifurcation are determined by applying the normal form theory and the center manifold argument.…”
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Rolling Bearing Fault Diagnosis Based on Domain Adaptation and Preferred Feature Selection under Variable Working Conditions by Xiao Yu, Wei Chen, Chuanlong Wu, Enjie Ding, Yuanyuan Tian, Haiwei Zuo, Fei Dong

“…In this framework, an improved domain adaptation method, transfer component analysis with preserving local manifold structure (TCAPLMS), is proposed to reduce the differences in the data distributions between different domain datasets and, at the same time, take the label information of feature dataset and the local manifold structure of feature data into consideration. …”
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An Automatic Recognition Method of Microseismic Signals Based on S Transformation and Improved Gaussian Mixture Model by Kaikai Wang, Chun’an Tang, Ke Ma, Xintang Wang, Qiang Li

“…S transform (ST) and Manifold Learning (ML) methods are introduced to extract the characteristics of the microseismic signals, and Gaussian Mixture Model based on the improved Bee Colony optimization algorithm (IBC-GMM) is established to identify the microseismic signals accurately. …”
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Stability and Hopf Bifurcation of an n-Neuron Cohen-Grossberg Neural Network with Time Delays by Qiming Liu, Sumin Yang

“…Moreover, the direction and stability of Hopf bifurcation are obtained by applying the normal form theory and the center manifold theorem. Numerical simulations are given to illustrate the obtained results.…”
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Hopf Bifurcation Analysis for the Model of the Chemostat with One Species of Organism by Haiyun Bai, Yanhui Zhai

“…By using the normal form theory and center manifold method, we derive the explicit formulas determining the stability and direction of bifurcating periodic solutions. …”
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Bifurcation of a Delayed SEIS Epidemic Model with a Changing Delitescence and Nonlinear Incidence Rate by Juan Liu

“…Directly afterwards, properties of the Hopf bifurcation are determined based on the normal form theory and the center manifold theorem. At last, numerical simulations are carried out to illustrate the obtained theoretical results.…”
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Lightlike Hypersurfaces of Indefinite Generalized Sasakian Space Forms by Dae Ho Jin

“…First we study the general theory for lightlike hypersurfaces of indefinite trans-Sasakian manifold of type (α,β). Next we prove several characterization theorems for lightlike hypersurfaces of an indefinite generalized Sasakian space form.…”
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Local Hopf Bifurcation in a Competitive Model of Market Structure with Consumptive Delays by Xuhui Li

“…The explicit formulas determining the stability and other properties of bifurcating periodic solutions are derived by using normal form theory and center manifold argument. Finally, numerical simulations are given to support the analytical results.…”
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Frobenius integrability of certain $p$-forms on singular spaces by Cao, Junyan, Höring, Andreas

“…Demailly proved that on a smooth compact Kähler manifold the distribution defined by a holomorphic $p$-form with values in an anti-pseudoeffective line bundle is always integrable. …”
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The action of pseudo-differential operators on functions harmonic outside a smooth hyper-surface by Boutet de Monvel, Louis, Colin de Verdière, Yves

“…The goal of this note is to describe the action of pseudo-differential operators on the space of square integrable functions which are harmonic outside a smooth closed hyper-surface of a compact Riemannian manifold.…”
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Some Inequalities for the Omori-Yau Maximum Principle by Kyusik Hong

“…Borbély’s condition for the conclusion of the Omori-Yau maximum principle for the Laplace operator on a complete Riemannian manifold to a second-order linear semielliptic operator L with bounded coefficients and no zeroth order term. …”
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Dynamics in a Delayed Neural Network Model of Two Neurons with Inertial Coupling by Changjin Xu, Peiluan Li

“…Applying the normal form theory and the center manifold argument, we derive the explicit formulas for determining the properties of the bifurcating periodic solutions. …”
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On the time-dependent parabolic wave equation by Arthur D. Gorman

“…We develop a Wentzel-Kramers-Brillouin (WKB) formalism to obtain the asymptotic solution in noncaustic regions and modify the Lagrange manifold formalism to obtain the asymptotic solution near caustics. …”
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Chaos and shadowing around a homoclinic tube by Yanguang (Charles) Li

“…F has a homoclinic tube asymptotic to an invariant manifold. Around the homoclinic tube, Bernoulli shift dynamics of submanifolds is established through a shadowing lemma. …”
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Stability and Bifurcation Analysis of a Three-Dimensional Recurrent Neural Network with Time Delay by Yingguo Li

“…Applying the nor- mal form method and center manifold theory, we obtain some local bifurcation results and derive formulas for determining the bifurcation direction and the stability of the bifurcated periodic solution. …”
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Why Scientific Policy Advice Is so Unpopular by Gisela Färber

“…Abstract The manifold special features and challenges of economic policy-advising are ultimately based on the principles of trust and mutual learning. …”
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Dynamic Properties of a Forest Fire Model by Na Min, Hongyang Zhang, Zhilin Qu

“…By using the normal form approach theory and center manifold theory, we analyze the stability of the trivial solution and Hopf bifurcation of this model. …”
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On the Computation of Degenerate Hopf Bifurcations for n-Dimensional Multiparameter Vector Fields by Michail P. Markakis, Panagiotis S. Douris

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

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

“…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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