Decoupling and disturbance decoupling of a class of homogeneous polynomial systems-A subspace approach

1987 ◽  
Author(s):  
Wijesuriya Dayawansa ◽  
Clyde Martin
Keyword(s):  
Homogeneous Polynomial ◽  
Polynomial Systems ◽  
Disturbance Decoupling

Center Problem for Quasi-Homogeneous Polynomial Systems with a Given Weight Degree

2018 ◽  
Vol 28 (14) ◽  
pp. 1850174 ◽  
Author(s):  
Yanqin Xiong ◽  
Jianqiang Hu ◽  
Shimin Li ◽  
Jingzheng Li
Keyword(s):  
Homogeneous Polynomial ◽  
Necessary Conditions ◽  
Sufficient Conditions ◽  
Polynomial Systems ◽  
Necessary And Sufficient Conditions ◽  
Center Problem ◽  
Necessary And Sufficient

This paper considers the center problem for quasi-homogeneous polynomial systems with a given weight degree. We provide the necessary conditions such that these systems have a center at the origin. Especially, we present the necessary and sufficient conditions on the existence of a center for some class of such systems.

An Improvement on the Number of Limit Cycles Bifurcating from a Nondegenerate Center of Homogeneous Polynomial Systems

2018 ◽  
Vol 28 (06) ◽  
pp. 1850078 ◽  
Author(s):  
Pei Yu ◽  
Maoan Han ◽  
Jibin Li
Keyword(s):  
Hopf Bifurcation ◽  
Normal Form ◽  
Limit Cycle ◽  
Limit Cycles ◽  
Correct Answer ◽  
Homogeneous Polynomial ◽  
Bifurcation Theory ◽  
Polynomial Systems ◽  
Homogeneous Polynomials ◽  
Appl Math

In the two articles in Appl. Math. Comput., J. Giné [2012a, 2012b] studied the number of small limit cycles bifurcating from the origin of the system: [Formula: see text], [Formula: see text], where [Formula: see text] and [Formula: see text] are homogeneous polynomials of degree [Formula: see text]. It is shown that the maximal number of the small limit cycles, denoted by [Formula: see text], satisfies [Formula: see text] for [Formula: see text]; and [Formula: see text], [Formula: see text]. It seems that the correct answer for their case [Formula: see text] should be [Formula: see text]. In this paper, we apply Hopf bifurcation theory and normal form computation, and perturb the isolated, nondegenerate center (the origin) to prove that [Formula: see text] for [Formula: see text]; and [Formula: see text] for [Formula: see text], which improve Giné’s results with one more limit cycle for each case.

Monodromy, center–focus and integrability problems for quasi-homogeneous polynomial systems

2010 ◽  
Vol 72 (3-4) ◽  
pp. 1726-1736 ◽  
Author(s):  
A. Algaba ◽  
E. Freire ◽  
E. Gamero ◽  
C. García
Keyword(s):  
Homogeneous Polynomial ◽  
Polynomial Systems
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