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   Articles with "quadratic vector" as a keyword



Structurally Unstable Quadratic Vector Fields of Codimension Two: Families Possessing Either a Cusp Point or Two Finite Saddle-Nodes

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recommendations! Published in 2020 at "Journal of Dynamics and Differential Equations"

DOI: 10.1007/s10884-020-09871-2

Abstract: The goal of this paper is to contribute to the classification of the phase portraits of planar quadratic differential systems according to their structural stability. Artes et al. (Mem Am Math Soc 134:639, 1998) proved… read more here.

Keywords: vector fields; structurally unstable; quadratic vector; phase portraits ... See more keywords

Quadratic vector fields in class I

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recommendations! Published in 2024 at "Dynamical Systems"

DOI: 10.1080/14689367.2024.2436223

Abstract: In [Ye et al., Theory of Limit Cycles, 1986], quadratic systems are classified into three different normal forms (I, II and III) with increasing number of parameters. The simplest family is I and even several… read more here.

Keywords: bifurcation; vector fields; phase portraits; class ... See more keywords

Three classes of quadratic vector fields for which the Kahan discretisation is the root of a generalised Manin transformation

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recommendations! Published in 2019 at "Journal of Physics A: Mathematical and Theoretical"

DOI: 10.1088/1751-8121/aaf51e

Abstract: We apply Kahan's discretisation method to three classes of 2-dimensional quadratic vector fields with quadratic, resp cubic, resp quartic Hamiltonians. We show that the maps obtained in this way can be geometrically understood as the… read more here.

Keywords: kahan discretisation; quadratic vector; vector fields; generalised manin ... See more keywords

3-dimensional piecewise linear and quadratic vector fields with invariant spheres

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recommendations! Published in 2024 at "Electronic Journal of Qualitative Theory of Differential Equations"

DOI: 10.14232/ejqtde.2024.1.43

Abstract: We consider the class X of 3 -dimensional piecewise smooth vector fields that admit a first integral which leaves invariant any sphere centered at the origin. In this class, we prove that a linear vector… read more here.

Keywords: vector; piecewise linear; vector fields; quadratic vector ... See more keywords