#### Filter Results:

- Full text PDF available (135)

#### Publication Year

1962

2017

- This year (5)
- Last five years (57)

#### Publication Type

#### Co-author

#### Publication Venue

#### Key Phrases

Learn More

In this paper, we prove the existence of twelve small (local) limit cycles in a planar system with third-degree polynomial functions. The best result so far in literature for a cubic order planar system is eleven limit cycles. The system considered in this paper has a saddle point at the origin and two focus points which are symmetric about the origin. This… (More)

In this paper, the existence of 12 small limit cycles is proved for cubic order Z 2-equivariant vector fields, which bifur-cate from fine focus points. This is a new result in the study of the second part of the 16th Hilbert problem. The system under consideration has a saddle point, or a node, or a focus point (including center) at the origin, and two weak… (More)

- Maoan Han, Yiping Lin, Pei Yu
- I. J. Bifurcation and Chaos
- 2004

The focus of the paper is mainly on the existence of limit cycles of a planar system with third-degree polynomial functions. A previously developed perturbation technique for computing normal forms of differential equations is employed to calculate the focus values of the system near equilibrium points. Detailed studies have been provided for a number of… (More)

- Zhiqiang Wu, Pei Yu, Keqi Wang
- I. J. Bifurcation and Chaos
- 2004

This paper investigates periodic bifurcation solutions of a mechanical system which involves a van der Pol type damping and a hysteretic damper representing restoring force. This system has recently been studied based on the singularity theory for bifurcations of smooth functions. However, the results do not actually take into account the property of… (More)

In this paper, we report the existence of twelve small limit cycles in a planar system with 3rd-degree polynomial functions. The system has Z 2-symmetry, with a saddle point, or a node, or a focus point at the origin, and two focus points which are symmetric about the origin. It is shown that such a Z 2-equivariant vector field can have twelve small limit… (More)

- Tsang-Chih Kuo, Ching-Ting Tan, +11 authors Min-Liang Kuo
- The Journal of clinical investigation
- 2013

Angiopoietin-like protein 1 (ANGPTL1) is a potent regulator of angiogenesis. Growing evidence suggests that ANGPTL family proteins not only target endothelial cells but also affect tumor cell behavior. In a screen of 102 patients with lung cancer, we found that ANGPTL1 expression was inversely correlated with invasion, lymph node metastasis, and poor… (More)

In this paper, a perturbation method based on multiple scales is used for computing the normal forms of nonlinear dynamical systems. The approach, without the application of center manifold theory, can be used to systematically find the explicit normal form of a system described by a general n-dimensional differential equation. The attention is focused on… (More)

- P. Yu, R. Corless
- 2009

Keywords: Hilbert's 16th problem Limit cycle Bifurcation Focus value Normal form Maple a b s t r a c t This paper is concerned with the practical complexity of the symbolic computation of limit cycles associated with Hilbert's 16th problem. In particular, in determining the number of small-amplitude limit cycles of a non-linear dynamical system, one often… (More)

- Jiao Jiang, Maoan Han, Pei Yu, Stephen Lynch
- I. J. Bifurcation and Chaos
- 2007

Liénard systems and their generalized forms are classical and important models of nonlinear oscillators, and have been widely studied by mathematicians and scientists. The main problem considered is the maximal number of limit cycles that the system can have. In this paper, two types of symmetric polynomial Liénard systems are investigated and the maximal… (More)

- Yuming Shi, Pei Yu
- 2005

This paper is concerned with chaos induced by strictly turbulent maps in noncompact sets of complete metric spaces. Two criteria of chaos for such types of maps are established, and then a criterion of chaos, characterized by snap-back repellers in complete metric spaces, is obtained. All the maps presented in this paper are proved to be chaotic either in… (More)