Results 261 to 270 of about 8,079,144 (302)

Twin Vector Fields and Independence of Spectra for Quadratic Vector Fields [PDF]

Journal of Dynamical and Control Systems, 2016
The object of this paper is to address the following question: When is a polynomial vector field on $\mathbb{C}^2$ completely determined (up to affine equivalence) by the spectra of its singularities? We will see that for quadratic vector fields this is not the case: given a generic quadratic vector field there is, up to affine equivalence, exactly one
Valente Ramírez
exaly   +3 more sources

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A smooth vector field for quadratic programming

2012 IEEE 51st IEEE Conference on Decision and Control (CDC), 2012
In this paper we consider the class of convex optimization problems with affine inequality constraints and focus hereby on the class of quadratic programs. We propose a smooth vector field that is constructed such that its trajectories converge to the saddle point of the Lagrangian function associated to the convex optimization problem.
Christian Ebenbauer, Hans-Bernd Dürr
exaly   +3 more sources

On the global analysis of the planar quadratic vector fields

Nonlinear Analysis: Theory, Methods & Applications, 1997
Using the concept of intersection multiplicity of projective curves, the author studies bifurcations of planar quadratic Hamiltonian systems (QHC). All bifurcation points (finite or infinite) of such systems are characterized by their intersection multiplicities.
Dana Schlomiuk
exaly   +2 more sources

Vector fields and quadratic maps

The Journal of the Acoustical Society of America, 1998
Vector fields describing responses of nonlinear systems are often investigated by sampling on a suitable Poincaré section. For example, period-1 limit cycles yield one fixed point, period-2 two points, and so on. More information could be obtained if the full return map on the section rather than just the fixed points were known.
Huw G. Davies, Konstantinos Karagiosis
openaire   +1 more source

Quadratic vector fields in class I

Dynamical Systems
In [Ye et al., Theory of Limit Cycles, 1986], quadratic systems are classified into three different normal forms (I, II and III) with increasing number of parameters. The simplest family is I and even several subfamilies of it have been studied, and some global attempts have been done, up to this paper, the full study was still undone. In this article,
Artés Ferragud, Joan Carles, Chen, Hebai, Ferrer, Lluc Manel, Jia, Man   +3 more
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Holomorphic Vector Fields and Quadratic Differentials on Planar Triangular Meshes [PDF]

, 2016
17 pages; final version, to appear in "Advances in Discrete Differential Geometry", ed. A. I.
Wai Yeung Lam, Ulrich Pinkall
exaly   +3 more sources

Bifurcation of critical periods from the rigid quadratic isochronous vector field [PDF]

Bulletin Des Sciences Mathematiques, 2008
This paper is concerned with the study of the number of critical periods of perturbed isochronous centers. More concretely, if X0 is a vector field having an isochronous center of period T0 at the point p and Xϵ is an analytic perturbation of X0 such ...
Armengol Gasull
exaly   +2 more sources

A Summary of Structurally Stable Quadratic Vector Fields

2018
To make this work self-contained, we are going to summarize in this chapter all the needed results from the paper of Artes et al. (Mem. Am. Math. Soc. 134(639), 1998). For the results of the present paper, the realizable structurally stable quadratic vector fields and the non-realizable ones are very important.
Joan C. Artés, Jaume Llibre, Alex C. Rezende   +2 more
openaire   +1 more source

A note on the completeness of homogeneous quadratic vector fields on the plane

Qualitative Theory of Dynamical Systems, 2005
The authors give a full description of the complete homogeneous quadratic vector fields defined on the plane. The main results obtained are as follows. Main results: Let \(F\) be a homogeneous quadratic vector field defined on the plane. Then the following assertions are equivalent: (1) \(F\) is complete; (2) \(F\) is quadratic-affine or the equation \(
Alberto Medina
exaly   +3 more sources