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Energy methods for lossless systems using quadratic differential forms. [PDF]
, 2008 In this thesis, we study the properties of lossless systems using the concept of quadratic differential forms (QDFs). Based on observation of physical linear lossless systems, we define a lossless system as one for which there exists a QDF known as an energy function that is positive along nonzero trajectories of the system and whose derivative along ...
Rao, Shodhan
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On Linear-Quadratic Differential Games for Fractional-Order Systems
Doklady Mathematics, 2023Summary: We consider a finite-horizon two-person zero-sum differential game in which the system dynamics is described by a linear differential equation with a Caputo fractional derivative and the goals of control of the players are, respectively, to minimize and maximize a quadratic terminal-integral cost function.
Gomoyunov, M. I., Lukoyanov, N. Yu.
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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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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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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 ...
Harish K. Pillai, Etar Rogers
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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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Invariants and symbolic calculations in the theory of quadratic differential systems
ACM Communications in Computer Algebra, 2011While quadratic differential systems intervene in many areas of applied mathematics and they also have theoretical importance, the topological classification of this class remains an extremely hard problem. However, in recent years much progress has been achieved due to the use of computer algebra and numerical calculations for obtaining complete ...
Dana Schlomiuk, Nicolae Vulpe
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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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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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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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