scholarly journals Limit cycle bifurcations in a planar piecewise quadratic system with multiple parameters

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Shuhua Gong ◽  
Maoan Han
Keyword(s):  
Limit Cycle ◽  
Quadratic System ◽  
Multiple Parameters

Limit cycle problem of quadratic system of type (III) m=0, (III)

2005 ◽  
Vol 20 (4) ◽  
pp. 431-440
Author(s):  
Ali Elamin ◽  
M. Saeed ◽  
Luo Dingjun
Keyword(s):  
Limit Cycle ◽  
Quadratic System ◽  
Type Iii

scholarly journals Quadratic systems with a degenerate critical point

1988 ◽  
Vol 38 (1) ◽  
pp. 1-10 ◽  
Author(s):  
W. A. Coppel
Keyword(s):  
Critical Point ◽  
Limit Cycle ◽  
Quadratic System ◽  
Quadratic Systems ◽  
Degenerate Critical Point

It is shown that a quadratic system with a degenerate critical point has at most one limit cycle.

scholarly journals Quadratic systems with a weak focus

1991 ◽  
Vol 44 (3) ◽  
pp. 511-526 ◽  
Author(s):  
Zhang Pingguang ◽  
Cai Suilin
Keyword(s):  
Singular Point ◽  
Limit Cycle ◽  
Limit Cycles ◽  
Relative Position ◽  
Quadratic System ◽  
Singular Points ◽  
Finite Plane ◽  
Quadratic Systems ◽  
Weak Focus

In this paper we study the number and the relative position of the limit cycles of a plane quadratic system with a weak focus. In particular, we prove the limit cycles of such a system can never have (2, 2)-distribution, and that there is at most one limit cycle not surrounding this weak focus under any one of the following conditions:(i) the system has at least 2 saddles in the finite plane,(ii) the system has more than 2 finite singular points and more than 1 singular point at infinity,(iii) the system has exactly 2 finite singular points, more than 1 singular point at infinity, and the weak focus is itself surrounded by at least one limit cycle.

scholarly journals Limit Cycles of a Class of Piecewise Smooth Liénard Systems

2016 ◽  
Vol 26 (01) ◽  
pp. 1650009 ◽  
Author(s):  
Lijuan Sheng
Keyword(s):  
Limit Cycle ◽  
Limit Cycles ◽  
Function Theory ◽  
Polynomial Systems ◽  
Melnikov Function ◽  
Piecewise Smooth ◽  
Piecewise Polynomial ◽  
Multiple Parameters ◽  
Liénard Systems ◽  
Limit Cycle Bifurcation

In this paper, we study the problem of limit cycle bifurcation in two piecewise polynomial systems of Liénard type with multiple parameters. Based on the developed Melnikov function theory, we obtain the maximum number of limit cycles of these two systems.

On the limit cycle bifurcation of a polynomial system from a global center

2014 ◽  
Vol 12 (03) ◽  
pp. 251-268 ◽  
Author(s):  
Yanqin Xiong ◽  
Maoan Han
Keyword(s):  
Limit Cycle ◽  
Polynomial System ◽  
Melnikov Function ◽  
Quadratic System ◽  
Hopf Bifurcations ◽  
First Order ◽  
Global Center ◽  
Limit Cycle Bifurcation

In this paper, we consider a quadratic system with a global center under polynomial perturbations of degree n(n ≥ 1). By using the first-order Melnikov function, we study Poincaré and Poincaré–Andronov–Hopf bifurcations. We prove that both Poincaré and Hopf cyclicity are n for n ≥ 2 up to the first order in ε.

scholarly journals On the limit cycle distribution over two nests in quadratic systems

1995 ◽  
Vol 52 (3) ◽  
pp. 461-474 ◽  
Author(s):  
Xianhua Huang ◽  
J.W. Reyn
Keyword(s):  
Limit Cycle ◽  
Critical Points ◽  
Limit Cycles ◽  
Affirmative Answer ◽  
Quadratic System ◽  
Quadratic Systems ◽  
Hilbert’S 16Th Problem ◽  
Hilbert's 16Th Problem

As a contribution to the solution of Hilbert's 16th problem the question is considered whether in a quadratic system with two nests of limit cycles at least in one nest there exists precisely one limit cycle. An affirmative answer to this question is given for the case that the sum of the multiplicities of the finite critical points in the system is equal to three.

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