Quadratic systems with definite singularities of total multiplicity at most one

2021 ◽  
pp. 263-280
Author(s):  
Joan C. Artés ◽  
Jaume Llibre ◽  
Dana Schlomiuk ◽  
Nicolae Vulpe
Keyword(s):  
Quadratic Systems ◽  
Total Multiplicity

scholarly journals Quadratic systems with invariant straight lines of total multiplicity two having Darboux invariants

2015 ◽  
Vol 17 (03) ◽  
pp. 1450018 ◽  
Author(s):  
Jaume Llibre ◽  
Regilene D. S. Oliveira
Keyword(s):  
Polynomial Systems ◽  
Quadratic Polynomial ◽  
Phase Portraits ◽  
Quadratic Systems ◽  
Total Multiplicity ◽  
Straight Lines

In this paper, we present the global phase portraits in the Poincaré disc of the planar quadratic polynomial systems which admit invariant straight lines with total multiplicity two and Darboux invariants.

scholarly journals On algebraic approach in quadratic systems

2008 ◽  
Author(s):  
Matej Mencinger ◽  
Marko Robnik ◽  
Valery Romanovski
Keyword(s):  
Algebraic Approach ◽  
Quadratic Systems

scholarly journals Wigner functions of quadratic systems

1982 ◽  
Vol 115 (1-2) ◽  
pp. 215-231 ◽  
Author(s):  
E.A. Akhundova ◽  
V.V. Dodonov ◽  
V.I. Man'ko
Keyword(s):  
Wigner Functions ◽  
Quadratic Systems

On the Pauli-Van Vleck formula for arbitrary quadratic systems with memory in one dimension

1985 ◽  
Vol 18 (17) ◽  
pp. L1071-L1073 ◽  
Author(s):  
L G Urrutia ◽  
J C D'Olivo ◽  
F Zertuche
Keyword(s):  
One Dimension ◽  
Quadratic Systems ◽  
Systems With Memory ◽  
Van Vleck ◽  
With Memory

A Class of Three-Dimensional Quadratic Systems with Ten Limit Cycles

2016 ◽  
Vol 26 (09) ◽  
pp. 1650149 ◽  
Author(s):  
Chaoxiong Du ◽  
Yirong Liu ◽  
Wentao Huang
Keyword(s):  
Hopf Bifurcation ◽  
Limit Cycles ◽  
Three Dimensional ◽  
Singular Value ◽  
Singular Points ◽  
Quadratic Systems ◽  
Symmetric Points ◽  
Fifth Order

Our work is concerned with a class of three-dimensional quadratic systems with two symmetric singular points which can yield ten small limit cycles. The method used is singular value method, we obtain the expressions of the first five focal values of the two singular points that the system has. Both singular symmetric points can be fine foci of fifth order at the same time. Moreover, we obtain that each one bifurcates five small limit cycles under a certain coefficient perturbed condition, consequently, at least ten limit cycles can appear by simultaneous Hopf bifurcation.

scholarly journals Local Bifurcations and a Survey of Bounded Quadratic Systems

2000 ◽  
Vol 165 (2) ◽  
pp. 430-467 ◽  
Author(s):  
Freddy Dumortier ◽  
Chris Herssens ◽  
Lawrence Perko
Keyword(s):  
Quadratic Systems ◽  
Local Bifurcations
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