Center condition and bifurcation of limit cycles for quadratic switching systems with a nilpotent equilibrium point

2021 ◽  
Vol 303 ◽  
pp. 326-368
Author(s):  
Ting Chen ◽  
Lihong Huang ◽  
Pei Yu
Keyword(s):  
Equilibrium Point ◽  
Limit Cycles ◽  
Switching Systems ◽  
Bifurcation Of Limit Cycles ◽  
Center Condition

Bifurcation of limit cycles at infinity in a class of switching systems

2016 ◽  
Vol 88 (1) ◽  
pp. 403-414 ◽  
Author(s):  
Feng Li ◽  
Yuanyuan Liu ◽  
Pei Yu
Keyword(s):  
Limit Cycles ◽  
Switching Systems ◽  
Bifurcation Of Limit Cycles

scholarly journals Bifurcation of Limit Cycles and Center Conditions for Two Families of Kukles-Like Systems with Nilpotent Singularities

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Peiluan Li ◽  
Yusen Wu ◽  
Xiaoquan Ding
Keyword(s):  
Hopf Bifurcation ◽  
Limit Cycles ◽  
Singular Points ◽  
Center Problem ◽  
Bifurcation Of Limit Cycles ◽  
Center Conditions

We solve theoretically the center problem and the cyclicity of the Hopf bifurcation for two families of Kukles-like systems with their origins being nilpotent and monodromic isolated singular points.

BIFURCATION OF LIMIT CYCLES AND ISOCHRONOUS CENTERS FOR A QUARTIC SYSTEM

2013 ◽  
Vol 23 (10) ◽  
pp. 1350172 ◽  
Author(s):  
WENTAO HUANG ◽  
AIYONG CHEN ◽  
QIUJIN XU
Keyword(s):  
Limit Cycles ◽  
Necessary Conditions ◽  
Polynomial System ◽  
Isochronous Center ◽  
Eighth Order ◽  
Bifurcation Of Limit Cycles ◽  
Quartic Polynomial ◽  
Fine Focus ◽  
Sufficient And Necessary Conditions ◽  
Isochronous Centers

For a quartic polynomial system we investigate bifurcations of limit cycles and obtain conditions for the origin to be a center. Computing the singular point values we find also the conditions for the origin to be the eighth order fine focus. It is proven that the system can have eight small amplitude limit cycles in a neighborhood of the origin. To the best of our knowledge, this is the first example of a quartic system with eight limit cycles bifurcated from a fine focus. We also give the sufficient and necessary conditions for the origin to be an isochronous center.

scholarly journals Hopf Bifurcation of Limit Cycles in Discontinuous Liénard Systems

2012 ◽  
Vol 2012 ◽  
pp. 1-27 ◽  
Author(s):  
Yanqin Xiong ◽  
Maoan Han
Keyword(s):  
Hopf Bifurcation ◽  
Limit Cycles ◽  
Special Form ◽  
Bifurcation Of Limit Cycles ◽  
Liénard Systems

We consider a class of discontinuous Liénard systems and study the number of limit cycles bifurcated from the origin when parameters vary. We establish a method of studying cyclicity of the system at the origin. As an application, we discuss some discontinuous Liénard systems of special form and study the cyclicity near the origin.

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