Singular points and limit cycles of the generalized Kukles polynomial differential system
Известия высших учебных заведений. Поволжский регион: Физико-математические науки, 2022 Background. Searching of numbers of Poincare limit cycles of polynomial dynamic systems belongs to second part of the 16th Gilbert problem, which is not solved in general.
I.N. Mal'kov, V.V. Machulis
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GLOBAL PHASE PORTRAITS OF SOME REVERSIBLE CUBIC CENTERS WITH COLLINEAR OR INFINITELY MANY SINGULARITIES [PDF]
International Journal of Bifurcation and Chaos, 2012 We study the reversible cubic vector fields of the form ẋ = -y + ax2+ bxy + cy2- y(x2+ y2), ẏ = x + dx2+ exy + fy2+ x(x2+ y2), having simultaneously a center at infinity and at the origin. In this paper, the subclass of these reversible systems having collinear or infinitely many singularities are classified with respect to topological equivalence.
Magdalena Caubergh +2 more
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GLOBAL PHASE PORTRAITS OF QUADRATIC POLYNOMIAL DIFFERENTIAL SYSTEMS WITH A SEMI-ELEMENTAL TRIPLE NODE [PDF]
International Journal of Bifurcation and Chaos, 2013 Planar quadratic differential systems occur in many areas of applied mathematics. Although more than one thousand papers have been written on these systems, a complete understanding of this family is still missing. Classical problems, and in particular, Hilbert's 16th problem [Hilbert, 1900, 1902], are still open for this family.
Joan C. Artés +2 more
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Combining global and multi-scale features in a description of the solar wind-magnetosphere coupling [PDF]
Annales Geophysicae, 2003 The solar wind-magnetosphere coupling during substorms exhibits dynamical features in a wide range of spatial and temporal scales. The goal of our work is to combine the global and multi-scale description of magnetospheric dynamics in a unified ...
A. Y. Ukhorskiy +4 more
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Time-Optimal Problem in the Roto-Translation Group with Admissible Control in a Circular Sector
Mathematics, 2023 We study a time-optimal problem in the roto-translation group with admissible control in a circular sector. The problem reveals the trajectories of a car model that can move forward on a plane and turn with a given minimum turning radius.
Alexey Mashtakov, Yuri Sachkov
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Global dynamics of a non-symmetric cubic Lienard system
四川大学学报. 自然科学版, 2022 In this paper, we study global dynamics of a cubic non-symmetric Lienard system with global parameters, i.e., parameters are not required to be sufficiently small.
SUN Shu-Ting, CHEN Xing-Wu
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Global Phase Portraits of Quadratic Systems with a Complex Ellipse as Invariant Algebraic Curve [PDF]
Acta Mathematica Sinica, English Series, 2017 In this paper we study a new class of quadratic systems and classify all its phase portraits. More precisely, we characterize the class of all quadratic polynomial differential systems in the plane having a complex ellipse x^2 y^2 1=0 as invariant algebraic curve.
Llibre, Jaume, Valls, Clàudia
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Using Convolutional Neural Network to Emulate Seasonal Tropical Cyclone Activity
Journal of Advances in Modeling Earth Systems, 2023 It has been widely recognized that tropical cyclone (TC) genesis requires favorable large‐scale environmental conditions. Based on these linkages, numerous efforts have been made to establish an empirical relationship between seasonal TC activities and ...
Dan Fu, Ping Chang, Xue Liu
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The phase portrait of the Hamiltonian system associated to a Pinchuk map
Anais da Academia Brasileira de CiênciasIn this paper we describe the global phase portrait of the Hamiltonian system associated to a Pinchuk map in the Poincaré disc. In particular, we prove that this phase portrait has 15 separatrices, five of them singular points, and 7 canonical regions ...
JOAN CARLES ARTÉS +2 more
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Global phase portraits of a degenerate Bogdanov-Takens system with symmetry (Ⅱ)
Discrete & Continuous Dynamical Systems - B, 2018 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Chen, Hebai, Chen, Xingwu
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