scholarly journals Darboux method and search of invariants for the Lotka–Volterra and complex quadratic systems

1999 ◽  
Vol 40 (4) ◽  
pp. 2074-2091 ◽  
Author(s):  
Laurent Cairó ◽  
Marc R. Feix ◽  
Jaume Llibre
Keyword(s):  
Quadratic Systems ◽  
Darboux Method

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

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

On the region of attraction of nonlinear quadratic systems

Automatica ◽  
2007 ◽  
Vol 43 (12) ◽  
pp. 2119-2123 ◽  
Author(s):  
F. Amato ◽  
C. Cosentino ◽  
A. Merola
Keyword(s):  
Region Of Attraction ◽  
Quadratic Systems

scholarly journals On the reduction of multivariate quadratic systems to best rank-1 approximation of three-way tensors

2016 ◽  
Vol 62 ◽  
pp. 9-15 ◽  
Author(s):  
Alex P. da Silva ◽  
Pierre Comon ◽  
André L.F. de Almeida
Keyword(s):  
Quadratic Systems
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