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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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Bifurcating limit cycles in quadratic polynomial differential systems
Physica A: Statistical Mechanics and its Applications, 2000Abstract We conducted a study on the plane quadratic polynomial differential systems with two or three parameters. Bifurcation curves were drawn in the cross-section of parameter space, dividing the section into several regions. Different number of limit cycles can be identified in different regions. Diagrams of variation of amplitude of limit cycles
H.S.Y. Chan, K.W. Chung, Dongwen Qi
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SOME BIFURCATION DIAGRAMS FOR LIMIT CYCLES OF QUADRATIC DIFFERENTIAL SYSTEMS
International Journal of Bifurcation and Chaos, 2001Concrete numerical examples of quadratic differential systems having three limit cycles surrounding one singular point are shown. In case another finite singular point also exists, a (3, 1) distribution of limit cycles is also obtained. This is the highest number of limit cycles known to occur in a quadratic differential system so far.
Chan, H. S. Y. +2 more
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