Results 31 to 40 of about 17,601,941 (298)

Complex dynamics of a sub-quadratic Lorenz-like system

Open Physics, 2023
Motivated by the generic dynamical property of most quadratic Lorenz-type systems that the unstable manifolds of the origin tending to the stable manifold of nontrivial symmetrical equilibria forms a pair of heteroclinic orbits, this technical note ...
Li Zhenpeng, Ke Guiyao, Wang Haijun, Pan Jun, Hu Feiyu, Su Qifang   +5 more
doaj   +1 more source

Alternative Theorems for Quadratic Inequality Systems and Global Quadratic Optimization [PDF]

SIAM Journal on Optimization, 2009
We establish alternative theorems for quadratic inequality systems. Consequently, we obtain Lagrange multiplier characterizations of global optimality for classes of nonconvex quadratic optimization problems. We present a generalization of Dine's theorem to a system of two homogeneous quadratic functions with a regular cone.
Vaithilingam Jeyakumar, Gue Myung Lee, Guoyin Li 0001   +2 more
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New Exploration of Phase Portrait Classification of Quadratic Polynomial Differential Systems Based on Invariant Theory

AppliedMath
After linear differential systems in the plane, the easiest systems are quadratic polynomial differential systems in the plane. Due to their nonlinearity and their many applications, these systems have been studied by many authors.
Joan Carles Artés, Laurent Cairó, Jaume Llibre   +2 more
doaj   +1 more source

Optimized fuzzy fractional-order linear quadratic tracking control for a nonlinear system

Results in Control and Optimization, 2023
In this paper, a novel fuzzy fractional-order Linear Quadratic Tracking (LQT) controller optimized by a Multi-Objective gray Wolf Algorithm (MOGWA) is designed for a 6 Degree-Of-Freedom (DOF) quadcopter flying system.
M.J. Mahmoodabadi, N. Rezaee Babak
doaj   +1 more source

Systems of quadratic forms.

Journal für die reine und angewandte Mathematik (Crelles Journal), 1984
Let \(u_ F(r)\) be the smallest integer such that every system of r quadratic forms in n variables, defined over a field F, has a nontrivial common zero if \(n>u_ F(r)\). Let \(u_ F(r)=\infty\) if no such integer exists. Then \(u_ F(r)\leq frac{1}{2}(r^ 2+r)u_ F(1)\) and there exist fields for which this bound is best possible when \(r=1,2,3\). If F is
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Quadratic systems with a symmetrical solution

Electronic Journal of Qualitative Theory of Differential Equations, 2018
In this paper we study the existence and uniqueness of limit cycles for so-called quadratic systems with a symmetrical solution: \begin{equation*} \begin{split} \frac{dx(t)}{dt}& = P_2(x,y) \equiv a_{00}+a_{10}x+a_{01}y+a_{20}x^2+a_{11}xy+a_{02}y^2 ...
Andre Zegeling, Robert Kooij
doaj   +1 more source

Adaptive Model Predictive Control of a Two-wheeled Robot Manipulator with Varying Mass

Measurement + Control, 2018
This paper presents the adaptive model predictive control approach for a two-wheeled robot manipulator with varying mass. The mass variation corresponds to the robot picking and placing objects or loads from one place to another.
Mert Önkol, Coşku Kasnakoğlu
doaj   +1 more source

Set simulations for quadratic systems

IEEE Transactions on Automatic Control, 2003
In this paper, we study the problem of propagating in time a bounding set for the state of a class of nonlinear quadratic systems. The sequence of bounding sets is called the set simulation of the system, and conveys useful information about the stability and qualitative behavior of the possible time responses of the system.
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Preimages of quadratic dynamical systems [PDF]

Involve, a Journal of Mathematics, 2011
For a quadratic endomorphism of the affine line defined over the rationals we consider the problem of bounding the number of rational points that eventually land at a given constant after iteration, called pre-images of the constant. In the article "Uniform Bounds on Pre-Images Under Quadratic Dynamical Systems," it was shown that the number of ...
Hutz, Benjamin, Hyde, Trevor, Krause, Benjamin   +2 more
openaire   +3 more sources

Phase portraits of separable quadratic systems and a bibliographical survey on quadratic systems

Expositiones Mathematicae, 2021
Although planar quadratic differential systems and their applications have been studied in more than one thousand papers, we still have no complete understanding of these systems. In this paper we have two objectives. First we provide a brief bibliographical survey on the main results about quadratic systems. Here we do not consider the applications of
Tao Li, Jaume Llibre
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