LIMIT CYCLES FOR TWO CLASSES OF PLANAR POLYNOMIAL DIFFERENTIAL SYSTEMS WITH UNIFORM ISOCHRONOUS CENTERS

2019 ◽  
Vol 9 (3) ◽  
pp. 943-961 ◽  
Author(s):  
Bo Huang ◽  
◽  
Wei Niu ◽  
◽  
◽  
...  
Keyword(s):  
Limit Cycles ◽  
Differential Systems ◽  
Polynomial Differential Systems ◽  
Isochronous Centers ◽  
Planar Polynomial Differential Systems

scholarly journals Limit Cycles Coming from Some Uniform Isochronous Centers

2016 ◽  
Vol 16 (2) ◽  
Author(s):  
Haihua Liang ◽  
Jaume Llibre ◽  
Joan Torregrosa
Keyword(s):  
Periodic Orbits ◽  
Limit Cycles ◽  
Hilbert Problem ◽  
Differential Systems ◽  
Polynomial Differential Systems ◽  
16Th Hilbert Problem ◽  
Isochronous Centers

AbstractThis article is about the weak 16th Hilbert problem, i.e. we analyze how many limit cycles can bifurcate from the periodic orbits of a given polynomial differential center when it is perturbed inside a class of polynomial differential systems. More precisely, we consider the uniform isochronous centersof degree

Limit Cycles for a Class of Zp-Equivariant Differential Systems

2020 ◽  
Vol 30 (08) ◽  
pp. 2050115
Author(s):  
Jing Gao ◽  
Yulin Zhao
Keyword(s):  
Differential System ◽  
Limit Cycles ◽  
Melnikov Function ◽  
Differential Systems ◽  
First Order ◽  
Polynomial Differential Systems ◽  
Number Of Zeros ◽  
Planar Polynomial Differential Systems

In this paper, we study a class of [Formula: see text]-equivariant planar polynomial differential systems [Formula: see text]. It is shown that for any [Formula: see text] there is a differential system of the above type having at least [Formula: see text] limit cycles. This is proved by estimating the number of zeros of the first-order Melnikov function.

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