Results 241 to 250 of about 375,845 (279)

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
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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.
Hans-Bernd Durr, Erkin Saka, Christian Ebenbauer   +2 more
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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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QUADRATIC VECTOR FIELDS EQUIVARIANT UNDER THE D₂ SYMMETRY GROUP

International Journal of Bifurcation and Chaos, 2013
Symmetry often plays an important role in the formation of complicated structures in the dynamics of vector fields. Here, we study a specific family of systems defined on ℝ3, which are invariant under the D2 symmetry group. Under the assumption that they are polynomial of degree at most two, they belong to a two-parameter family of vector fields ...
Anastassiou, Stavros, Pnevmatikos, Spyros, Bountis, Tassos   +2 more
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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.
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Twelve Limit Cycles in 3D Quadratic Vector Fields with Z3 Symmetry

International Journal of Bifurcation and Chaos, 2018
This paper is concerned with the number of limit cycles bifurcating in three-dimensional quadratic vector fields with [Formula: see text] symmetry. The system under consideration has three fine focus points which are symmetric about the [Formula: see text]-axis.
Laigang Guo, Pei Yu, Yufu Chen
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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
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Quadratic vector fields with finitely many periodic orbits

1983
We prove that vector fields outside an algebraic hypersurface in the space of coefficients of quadratic vector fields in the plane have a finite number of periodic orbits.
J. Sotomayor, R. Paterlini
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Singular Perturbations Arising in Hilbert's 16th Problem for Quadratic Vector Fields

ZAMM, 1998
The author surveys some approaches to derive results on the maximal number of limit cycles for two-dimensional quadratic vector fields: normal forms, global desingularization, cyclicity of limit periodic sets. As an example the author considers a degenerate logarithmic spiral.
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Structurally stable quadratic vector fields

Memoirs of the American Mathematical Society, 1998
Joan C. Artés, Robert E. Kooij, Jaume Llibre   +2 more
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