Structurally Unstable Quadratic Vector Fields of Codimension Two: Families Possessing Either a Cusp Point or Two Finite Saddle-Nodes
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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
Phase Portraits of Dynamical Equations of Motion of a Rigid Body in a Resistive Medium
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DOI: 10.1007/s10958-018-3935-5
Abstract: We consider a mathematical model of the influence of a medium on a rigid body with a specific shape of its surface. In this model, we take into account the additional dependence of the moment… read more here.
Keywords: rigid body; medium; equations motion; phase portraits ... See more keywords
Phase Portraits of Random Planar Homogeneous Vector Fields
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DOI: 10.1007/s12346-020-00437-7
Abstract: In this paper, we study the probability of occurrence of phase portraits in the set of random planar homogeneous polynomial vector fields, of degree n . In particular, for $$n=1,2,3,$$ n = 1 , 2… read more here.
Keywords: random planar; planar homogeneous; portraits random; vector fields ... See more keywords
Phase portraits of separable quadratic systems and a bibliographical survey on quadratic systems
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DOI: 10.1016/j.exmath.2021.01.003
Abstract: Abstract Although planar quadratic differential systems and their applications have been studied in more than one thousand papers, we still have no complete understanding of these systems. In this paper we have two objectives. First… read more here.
Keywords: differential systems; separable quadratic; quadratic systems; bibliographical survey ... See more keywords
Darboux polynomials and global phase portraits for the D2 vector field
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DOI: 10.1016/j.jmaa.2018.12.043
Abstract: We study a vector field of R^3 equivariant under the D_2 symmetry group, called "the D_2 field" in the literature. We construct the complete list of Darboux polynomials for it, solving the partial differential equation… read more here.
Keywords: vector field; field; polynomials global; global phase ... See more keywords
Phase portraits and bifurcation diagram of the Gray-Scott model
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DOI: 10.1016/j.jmaa.2020.124840
Abstract: Abstract We give a complete classification of the phase portraits in the Poincar e ´ disk for the cubic polynomial systems x ˙ = 1 − x − a x y 2 , y ˙… read more here.
Keywords: bifurcation diagram; gray scott; phase portraits; scott model ... See more keywords
Phase portraits of Abel quadratic differential systems of the second kind
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DOI: 10.1080/14689367.2017.1402296
Abstract: ABSTRACT We provide normal forms and the global phase portraits on the Poincaré disk of some Abel quadratic differential equations of the second kind. Moreover, we also provide the bifurcation diagrams for these global phase… read more here.
Keywords: second kind; abel quadratic; phase portraits; quadratic differential ... See more keywords
Phase portraits of two classes of quadratic differential systems exhibiting as solutions two cubic algebraic curves
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DOI: 10.1515/dema-2022-0218
Abstract: Abstract The classification of the phase portraits is one of the classical and difficult problems in the qualitative theory of polynomial differential systems in R 2 {{\mathbb{R}}}^{2} , particularly for quadratic systems. Even with the… read more here.
Keywords: algebraic curves; differential systems; two classes; portraits two ... See more keywords
Global Phase Portraits for the Abel Quadratic Polynomial Differential Equations of the Second Kind With Z2-symmetries
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DOI: 10.4153/cmb-2017-026-6
Abstract: Abstract We provide normal forms and the global phase portraits on the Poincaré disk for all Abel quadratic polynomial diòerential equations of the second kind with ${{\mathbb{Z}}_{2}}$ -symmetries. read more here.
Keywords: second kind; global phase; equations second; quadratic polynomial ... See more keywords