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

Applied Mathematics Letters ◽

10.1016/j.aml.2016.06.006 ◽

2016 ◽

Vol 62 ◽

pp. 9-15 ◽

Cited By ~ 1

Author(s):

Alex P. da Silva ◽

Pierre Comon ◽

André L.F. de Almeida

Keyword(s):

Quadratic Systems

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Stability analysis and guaranteed cost control for stochastic nonlinear quadratic systems

2015 European Control Conference (ECC) ◽

10.1109/ecc.2015.7330704 ◽

2015 ◽

Author(s):

Alessio Merola ◽

Francesco Amato

Keyword(s):

Stability Analysis ◽

Cost Control ◽

Guaranteed Cost Control ◽

Quadratic Systems ◽

Guaranteed Cost

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On algebraic approach in quadratic systems

10.1063/1.3046248 ◽

2008 ◽

Author(s):

Matej Mencinger ◽

Marko Robnik ◽

Valery Romanovski

Keyword(s):

Algebraic Approach ◽

Quadratic Systems

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Wigner functions of quadratic systems

Physica A Statistical Mechanics and its Applications ◽

10.1016/0378-4371(82)90137-6 ◽

1982 ◽

Vol 115 (1-2) ◽

pp. 215-231 ◽

Cited By ~ 17

Author(s):

E.A. Akhundova ◽

V.V. Dodonov ◽

V.I. Man'ko

Keyword(s):

Wigner Functions ◽

Quadratic Systems

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

Journal of Physics A General Physics ◽

10.1088/0305-4470/18/17/002 ◽

1985 ◽

Vol 18 (17) ◽

pp. L1071-L1073 ◽

Cited By ~ 1

Author(s):

L G Urrutia ◽

J C D'Olivo ◽

F Zertuche

Keyword(s):

One Dimension ◽

Quadratic Systems ◽

Systems With Memory ◽

Van Vleck ◽

With Memory

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

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127416501492 ◽

2016 ◽

Vol 26 (09) ◽

pp. 1650149 ◽

Cited By ~ 5

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.

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