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UNCERTAIN SYSTEMS, BEHAVIOURS AND QUADRATIC DIFFERENTIAL FORMS [PDF]

IFAC Proceedings Volumes, 2002
Abstract This paper considers uncertain systems from a behavioural point of view defined via quadratic differential forms. This uncertainty definition is closely related to the integral quadratic constraint uncertainty description commonly found in robust control theory.
Ian R. Petersen, Jan C. Willems
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The Moduli Spaces of Parabolic Connections with a Quadratic Differential and Isomonodromic Deformations [PDF]

, 2017
In this paper, we study the moduli spaces of parabolic connections with a quadratic differential. We endow these moduli spaces with symplectic structures by using the fundamental 2-forms on the moduli spaces of parabolic connections (which are phase ...
Komyo, Arata
core   +3 more sources

Exactly Solvable Quadratic Differential Equation Systems Through Generalized Inversion

Qualitative Theory of Dynamical Systems, 2023
AbstractWe study the autonomous systems of quadratic differential equations of the form $${\dot{x}}_i(t)={\textbf{x}}(t)^T {\textbf{A}}_i {\textbf{x}}(t) + {\textbf{v}}_i^T {\textbf{x}}(t)$$ x ˙ i
Bácsi, Ádám, Kocsis, Albert Tihamér
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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, Dana Schlomiuk, Ana Maria Travaglini   +2 more
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On the configurations of the singular points and their topological indices for the spatial quadratic polynomial differential systems

Journal of Differential Equations, 2020
Using the Euler-Jacobi formula there is a relation between the singular points of a polynomial vector field and their topological indices. Using this formula we obtain the configuration of the singular points together with their topological indices for ...
J. Llibre, C. Valls
semanticscholar   +1 more source

Phase portraits of two classes of quadratic differential systems exhibiting as solutions two cubic algebraic curves

Demonstratio Mathematica, 2023
The classification of the phase portraits is one of the classical and difficult problems in the qualitative theory of polynomial differential systems in R2{{\mathbb{R}}}^{2}, particularly for quadratic systems.
Benterki Rebiha, Belfar Ahlam
doaj   +1 more source

Symmetry of Quadratic Homogeneous Differential Systems

, 2008
10 ...
Nadjafikhah, Mehdi, Mahdipour-Shirayeh, Ali   +1 more
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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.
openaire   +1 more source

Rigid Polynomial Differential Systems with Homogeneous Nonlinearities

Mathematics
Planar differential systems whose angular velocity is constant are called rigid or uniform differential systems. The first rigid system goes back to the pendulum clock of Christiaan Huygens in 1656; since then, the interest for the rigid systems has been
Jaume Llibre
doaj   +1 more source

Quadratic systems with two invariant real straight lines and an invariant parabola

Electronic Journal of Qualitative Theory of Differential Equations
After the linear differential systems in the plane the easiest ones are the quadratic polynomial differential systems. Due to their nonlinearity and also to their many applications these systems have been studied by many authors. Let QS denote the set of
Jaume Llibre, Huaxin Ou
doaj   +1 more source