Results 11 to 20 of about 10,383,907 (288)
Algebraic limit cycles for quadratic polynomial differential systems [PDF]
Discrete and Continuous Dynamical Systems - B, 2018 AbstractAlgebraic limit cycles in quadratic polynomial differential systems started to be studied in 1958, and a few years later the following conjecture appeared: quadratic polynomial differential systems have at most one algebraic limit cycle. We prove that a quadratic polynomial differential system having an invariant algebraic curve with at most ...
Llibre, Jaume, Valls, Clàudia
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Models for Quadratic Algebras Associated with Second Order Superintegrable Systems in 2D [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2008 There are 13 equivalence classes of 2D second order quantum and classical superintegrable systems with nontrivial potential, each associated with a quadratic algebra of hidden symmetries.
Sarah Post +2 more
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Phase Portraits of Families VII and VIII of the Quadratic Systems
Axioms, 2023 The quadratic polynomial differential systems in a plane are the easiest nonlinear differential systems. They have been studied intensively due to their nonlinearity and the large number of applications.
Laurent Cairó, Jaume Llibre
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Hamiltonian and Variational Linear Distributed Systems [PDF]
, 2002 We use the formalism of bilinear- and quadratic differential forms in order to study Hamiltonian and variational linear distributed systems. It was shown in [1] that a system described by ordinary linear constant-coefficient differential equations is ...
Rapisarda, P. +7 more
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Stability of the Planar Quadratic Systems from the Ring-Theoretic Viewpoint
Mathematics, 2022 We show that the classical result on the stability of the origin in a quadratic planar system of ODEs can be formulated using either matrix theory or via its associated real and complex Marcus algebra.
Borut Zalar, Matej Mencinger
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The acyclicity of a quadratic differential system
Вестник Адыгейского государственного университета, серия «Естественно-математические и технические науки», 2021 Дан краткий обзор некоторых основных публикаций, посвященных исследованию вопроса о предельных циклах и сепаратрисах квадратичных дифференциальных систем. Рассмотрено наличие замкнутых траекторий для определенного класса автономных квадратичных систем на плоскости.
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On the relationship between nonlinear and linear differential systems
上海师范大学学报. 自然科学版, 2015 In this article, we establish the relationship between the quadratic time-varying differential systems and the linear systems, giving the sufficient conditions for the quadratic systems to have the reflecting function in the form of fractional function ...
ZHOU Zhengxin +4 more
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Reduction Methods and Chaos for Quadratic Systems of Differential Equations [PDF]
Studies in Applied Mathematics, 2015 We consider systems of differential equations with quadratic nonlinearities having applications for biochemistry and population dynamics, which may have a large dimension n. Due to the complexity of these systems, reduction algorithms play a crucial role in study of their large time behavior.
Vakulenko, S., Grigoriev, D., Weber, A.
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Geometry and integrability of quadratic systems with invariant hyperbolas
Electronic Journal of Qualitative Theory of Differential Equations, 2021 Let QSH be the family of non-degenerate planar quadratic differential systems possessing an invariant hyperbola. We study this class from the viewpoint of integrability.
Regilene Oliveira +2 more
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Geometry of quadratic differential systems in the neighborhood of infinity
Journal of Differential Equations, 2005 In this article we consider the behavior in the vicinity of infinity of the class of all planar quadratic differential systems. This family depends on twelve parameters but due to action of the affine group and re-scaling of time the family actually depends on five parameters.
Schlomiuk, Dana, Vulpe, Nicolae
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