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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.
Адам Дамирович Ушхо +2 more
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Synthesis of dissipative systems using quadratic differential forms: Part I [PDF]
IEEE Transactions on Automatic Control, 2002 In this second part of this paper, we discuss several important special cases of the problem solved in Part I. These are: disturbance attenuation and passivation, the full information case, the filtering problem, and the case that the to-be-controlled plant is given in input–state–output representation.
Trentelman, H.L., Willems, Jan C.
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Abel quadratic differential systems of second kind
Electronic Journal of Differential EquationsThe Abel differential equations of second kind, named after Niels Henrik Abel, are a class of ordinary differential equations studied by many authors. Here we consider the Abel quadratic polynomial differential equations of second kind denoting this class by \(QS_{Ab}\).
Artes, J.C. +3 more
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Maximum principle for a stochastic delayed system involving terminal state constraints [PDF]
Journal of Inequalities and Applications, 2017 We investigate a stochastic optimal control problem where the controlled system is depicted as a stochastic differential delayed equation; however, at the terminal time, the state is constrained in a convex set.
Jiaqiang Wen, Yufeng Shi
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Two-Variable Wilson Polynomials and the Generic Superintegrable System on the 3-Sphere [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2011 We show that the symmetry operators for the quantum superintegrable system on the 3-sphere with generic 4-parameter potential form a closed quadratic algebra with 6 linearly independent generators that closes at order 6 (as differential operators ...
Ernie G. Kalnins +2 more
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On point-dissipative systems of differential equations with quadratic nonlinearity [PDF]
International Journal of Mathematics and Mathematical Sciences, 1991 The system x′=Ax+f(x) of nonlinear vector differential equations, where the nonlinear term f(x) is quadratic with orthogonality property xTf(x)=0 for all x, is point-dissipative if ...
Anile K. Bose +2 more
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Bifurcations of the Riccati Quadratic Polynomial Differential Systems [PDF]
International Journal of Bifurcation and Chaos, 2021 In this paper, we characterize the global phase portrait of the Riccati quadratic polynomial differential system [Formula: see text] with [Formula: see text], [Formula: see text] nonzero (otherwise the system is a Bernoulli differential system), [Formula: see text] (otherwise the system is a Liénard differential system), [Formula: see text] a ...
Jaume Llibre +2 more
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Algebraic limit cycles for quadratic polynomial differential systems [PDF]
Discrete & 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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Critical Transitions in Piecewise Uniformly Continuous Concave Quadratic Ordinary Differential Equations [PDF]
Journal of Dynamics and Differential Equations, 2021 A critical transition for a system modelled by a concave quadratic scalar ordinary differential equation occurs when a small variation of the coefficients changes dramatically the dynamics, from the existence of an attractor–repeller pair of hyperbolic ...
Iacopo P. Longo, C. N'unez, R. Obaya
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Electronic Journal of Qualitative Theory of Differential Equations, 2021 During the last forty years the theory of integrability of Darboux, in terms of algebraic invariant curves of polynomial systems has been very much extended and it is now an active area of research.
Regilene Oliveira +3 more
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