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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Introduction. Palmyre-Tadmor : le patrimoine culturel en guerre by Sylvie Crogiez-Pétrequin

“…The heritage of mankind, as defined by Unesco, is considered to be a common asset for all humanity, threatened by armed conflict, even if the dangers to archaeological and architectural heritage remain manifold. After its instrumentalization by the Syrian Baathist regime, the destruction by Daech of Palmyra’s archaeological heritage, perceived as a symbol of both Western civilization and the national identity of the Syrian state, is thus destined to shock Westerners, just as the use of Palmyra was envisaged by the Syrian state in the construction of the Syrian national novel.…”
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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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Bifurcation Analysis in a Kind of Fourth-Order Delay Differential Equation by Xiaoqian Cui, Junjie Wei

“…Then the direction and stability of the Hopf bifurcation are determined, using the normal form method and the center manifold theorem. Finally, some numerical simulations are carried out to illustrate the analytic results.…”
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Screen conformal half-lightlike submanifolds by K. L. Duggal, B. Sahin

“…We study some properties of a half-lightlike submanifold M, of a semi-Riemannian manifold, whose shape operator is conformal to the shape operator of its screen distribution. …”
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Stability and bifurcation of numerical discretization Nicholson blowflies equation with delay by Xiaohua Ding, Wenxue Li

“…Applying the theory of normal form and center manifold, we not only discuss the linear stability of the equilibrium and the existence of the local Hopf bifurcations, but also give the explicit algorithm for determining the direction of bifurcation and stability of the periodic solution of bifurcation.…”
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Hopf Bifurcation and Chaos of a Delayed Finance System by Xuebing Zhang, Honglan Zhu

“…Furthermore, formulas for determining the direction of Hopf bifurcation and the stability of the bifurcating periodic solutions are derived by applying the normal form method and center manifold theorem. Finally, numerical simulation results are presented to validate the theoretical analysis. …”
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Stability and Hopf Bifurcation in a Diffusive Predator-Prey System with Beddington-DeAngelis Functional Response and Time Delay by Yuzhen Bai, Xiaopeng Zhang

“…Finally, the direction and stability of Hopf bifurcations are determined by normal form theory and center manifold reduction for partial functional differential equations.…”
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The Bifurcation of Two Invariant Closed Curves in a Discrete Model by Yingying Zhang, Yicang Zhou

“…The conditions for existence of these bifurcations are derived by using the center manifold and bifurcation theory. Numerical simulations and bifurcation diagrams exhibit the complex dynamical behaviors, especially the occurrence of two invariant closed curves.…”
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Some invariant theorems on geometry of Einstein non-symmetric field theory by Liu Shu-Lin, Xu Sen-Lin

“…It is shown that under the transformation TΛ:Uikℓ→U¯ikℓ≡Uikℓ+δiℓΛk−δkℓΛi, curvature tensor Skℓmi(U), Ricci tensor Sik(U), and scalar curvature S(U) are all invariant, where Λ=Λjdxj is a closed 1-differential form on an n-dimensional manifold M.…”
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Multiple Positive Solutions for Semilinear Elliptic Equations with Sign-Changing Weight Functions in ℝ𝑁 by Tsing-San Hsu

“…The study is based on the extraction of the Palais-Smale sequences in the Nehari manifold.…”
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« The Encantadas » ou le décompte du temps en archipel by Michel Imbert

“…This article endeavors to unravel the various strands or strata of time in Herman Melville’s novella, “The Encantadas,” and uncover the manifold layers of the text and its intertextual interplay. …”
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Fermat's principle in general relativity via Herglotz variational formalism by Joanna Piwnik, Joanna Gonera, Piotr Kosiński

“…It is based on Herglotz extension of canonical formalism and simple relation between the dynamics described by the Lagrangians homogeneous in velocities and the reduced dynamics on lower-dimensional configuration manifold. This approach is more flexible as it allows to extend immediately the Fermat principle to the case of massive particles and to eliminate any space-time coordinate, not only x0.…”
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