Results 31 to 40 of about 23,327 (265)
The Number of Limit Cycles of a Polynomial System on the Plane
Abstract and Applied Analysis, 2013 We perturb the vector field x˙=-yC(x,y), y˙=xC(x,y) with a polynomial perturbation of degree n, where C(x,y)=(1-y2)m, and study the number of limit cycles bifurcating from the period annulus surrounding the origin.
Chao Liu, Maoan Han
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The Investigation of Nonlinear Polynomial Control Systems
Моделирование и анализ информационных систем, 2021 The paper considers methods for estimating stability using Lyapunov functions, which are used for nonlinear polynomial control systems. The apparatus of the Gro¨bner basis method is used to assess the stability of a dynamical system. A description of the
Sergei Nikolaevich Chukanov +1 more
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Projections of Polynomial Vector Fields and the Poincaré Sphere
Journal of Differential Equations, 1997 Let \(p:\mathbb{R}^n\to\mathbb{R}^n\) be a homogeneous polynomial vector function, and let \(\rho:\mathbb{R}^n \to\mathbb{R}\) be a homogeneous polynomial of positive degree \(d\). The authors introduce the projection of \(p\) with respect to \(\rho\) by the formula \[ p^{\rho}(x)=- {\textstyle\frac{1}{d}} L_p(\rho)(x)x+\rho(x)p(x), \] where \(L_p(\rho)
Röhrl, Helmut, Walcher, Sebastian
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Symbolic Computations of First Integrals for Polynomial Vector Fields [PDF]
Foundations of Computational Mathematics, 2019 In this article we show how to generalize to the Darbouxian, Liouvillian and Riccati case the extactic curve introduced by J. Pereira. With this approach, we get new algorithms for computing, if it exists, a rational, Darbouxian, Liouvillian or Riccati first integral with bounded degree of a polynomial planar vector field.
Chèze, Guillaume, Combot, Thierry
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Poincaré Bifurcations of Two Classes of Polynomial Systems
Abstract and Applied Analysis, 2013 Using bifurcation methods and the Abelian integral, we investigate the number of the limit cycles that bifurcate from the period annulus of the singular point when we perturb the planar ordinary differential equations of the form , with an arbitrary ...
Jing Wang, Shuliang Shui
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Renormalization of vector fields with mass-like coupling in curved spacetime
European Physical Journal C: Particles and Fields, 2019 Using the method of covariant symbols we compute the divergent part of the effective action of the Proca field with non-minimal mass term. Specifically a quantum abelian vector field with a non-derivative coupling to an external tensor field in curved ...
C. Garcia-Recio, L. L. Salcedo
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3D Mesh Model Classification with a Capsule Network
Algorithms, 2021 With the widespread success of deep learning in the two-dimensional field, how to apply deep learning methods from two-dimensional to three-dimensional field has become a current research hotspot.
Yang Zheng +4 more
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Topological enumeration of complex polynomial vector fields [PDF]
Ergodic Theory and Dynamical Systems, 2014 AbstractThe enumeration of combinatorial classes of the complex polynomial vector fields in$ \mathbb{C} $presented by K. Dias [Enumerating combinatorial classes of the complex polynomial vector fields in$ \mathbb{C} $.Ergod. Th. & Dynam. Sys. 33(2013), 416–440] is extended here to a closed form enumeration of combinatorial classes for degree$d ...
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Advanced Engineering Materials, EarlyView.We develop a data‐driven method to derive the mathematical expressions of the Flory–Huggins interaction parameter χ for the swelling behavior of temperature–responsive hydrogels. Starting from initial assumptions of χ, our workflow combines Bayesian optimization, Flory–Rehner theory, and symbolic regression to generate candidate χ expressions.
Yawen Wang +2 more
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An Exponential Formula for Polynomial Vector Fields
Advances in Mathematics, 1997 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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