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Survey of results on quadratic differential systems
2021Quadratic differential systems occur often in many areas of applied mathematics, in population dynamics [145], nonlinear mechanics [236, 237, 69], chemistry, electrical circuits, neural networks, laser physics, hydrodynamics [347, 328, 183, 191], astrophysics [80] and others [280, 154, 102].
Joan C. Artés +3 more
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Blow-up solutions of quadratic differential systems
Journal of Mathematical Sciences, 2008zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Baris, J., Baris, P., Ruchlewicz, B.
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Two Dimensional Homogeneous Quadratic Differential Systems
SIAM Review, 1978The two-dimensional quadratic differential system (QDS) \[ \begin{gathered} \dot x = a_1 x^2 + b_1 xy + c_1 y^2 , \hfill \\ \dot y = a_2 x^2 + b_2 xy + c_2 y^2 \hfill \\ \end{gathered} \] where $( \cdot ) = {d} / {dt}$ and the coefficients are real constants is considered.
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Bifurcation Analysis in Planar Quadratic Differential Systems with Boundary
International Journal of Bifurcation and Chaos, 2020Given a planar quadratic differential system delimited by a straight line, we are interested in studying the bifurcation phenomena that can arise when the position on the boundary of two tangency points are considered as parameters of bifurcation. First, under generic conditions, we find a two-parametric family of quadratic differential systems with ...
Jocelyn A. Castro, Fernando Verduzco
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On the Limit Cycles of Quadratic Differential Systems
Acta Mathematica Sinica, English Series, 2002Here, the author gives necessary and sufficient conditions for all finite critical points of the quadratic differential system \[ \dot{x}=dy+\delta x+lx^2+mxy+ny^2, \qquad \dot{y}=x(1+ax+by) , \tag{Q} \] to be weak foci, and he solves an open problem stated by Yanqian Ye.
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On quadratic differential forms for n-D systems
Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187), 2002A study of quadratic differential forms for 1-D systems was carried out in Willems and Trentelman (1998). Extention and study of this concept of quadratic differential forms to n-D systems is the main purpose of the paper. This extension opens the way to generalization of several concepts of 1-D systems, like that of conservative systems and ...
H.K. Pillai, E. Rogers
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Polynomial inverse integrating factors for quadratic differential systems
Nonlinear Analysis: Theory, Methods & Applications, 2010The authors consider the real planar quadratic polynomial system \[ \dot x = P(x,y), \quad \dot y = Q(x,y), \tag{1} \] where the dot denotes the derivative with respect to the time variable, and \(P,Q\) are quadratic polynomials. A function \(R(x,y)\) is called integrating factor of system (1), if \(R\) is a solution of the equation \(\text{div}(RP,RQ)
Coll, Bartomeu +2 more
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Krylov subspace approximation for quadratic-bilinear differential system
International Journal of Systems Science, 2018AbstractMany nonlinear systems with nonlinearities of the form 1/(k+x), ex, xα, ln(x) can be converted into quadratic-bilinear differential algebraic equations (QBDAEs) by introducing new variables and operating some algebra computations. Previous researches claim that the first two generalised transfer functions are enough to capture the dynamical ...
Jun-Man Yang, Yao-Lin Jiang
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Robustness properties of linear quadratic hereditary differential systems
1982 21st IEEE Conference on Decision and Control, 1982In this paper we present a derivation of the Kalman frequency domain inequality, and also the corresponding equality, for the linear quadratic hereditary differential (LQHD) system. As a result, robustness properties of the LQHD system can be dealt with in an efficient manner.
W. Lee, B. Levy
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Linear Nonautonomous Systems of Differential Equations with a Quadratic Integral
Differential Equations, 2021The author considers the linear nonautonomous system of differential equations \[\dot x=A(t)x,\quad x\in \mathbb{R}^n,\tag{1}\] admitting the quadratic integral \[F(x,t)=(B(t)x,x)/2\tag{2}\] where the bracket (,) stands for the inner product on \(\mathbb{R}^n\).
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