Twelve Limit Cycles in 3D Quadratic Vector Fields with Z3 Symmetry

This paper is concerned with the number of limit cycles bifurcating in three-dimensional quadratic vector fields with Z3 symmetry. The system under consideration has three fine focus points which a...

[1]  Changbo Chen,et al.  An Application of Regular Chain Theory to the Study of Limit cycles , 2013, Int. J. Bifurc. Chaos.

[2]  Yirong Liu,et al.  A Class of Three-Dimensional Quadratic Systems with Ten Limit Cycles , 2016, Int. J. Bifurc. Chaos.

[3]  Pei Yu,et al.  Ten limit cycles around a center-type singular point in a 3-d quadratic system with quadratic perturbation , 2015, Appl. Math. Lett..

[4]  Liu Yi-Reng,et al.  THEORY OF VALUES OF SINGULAR POINT IN COMPLEX AUTONOMOUS DIFFERENTIAL SYSTEMS , 1990 .

[5]  William F. Langford,et al.  Degenerate Hopf bifurcation formulas and Hilbert's 16th problem , 1989 .

[6]  Hopf bifurcation for a class of three-dimensional nonlinear dynamic systems , 2010 .

[7]  Y. Ilyashenko,et al.  Finitely-smooth normal forms of local families of diffeomorphisms and vector fields , 1991 .

[8]  S. Smale.  Mathematical problems for the next century , 1998 .

[9]  Pei Yu,et al.  Twelve limit cycles around a singular point in a planar cubic-degree polynomial system , 2014, Commun. Nonlinear Sci. Numer. Simul..

[10]  J. Carr.  Applications of Centre Manifold Theory , 1981 .

[11]  Pei Yu,et al.  A study on Zoladek's example , 2011 .

[12]  Bifurcation of ten small-amplitude limit cycles by perturbing a quadratic Hamiltonian system with cubic polynomials , 2013, 1311.3381.

[13]  Yun Tian,et al.  An Explicit Recursive Formula for Computing the Normal Form and Center Manifold of General n-Dimensional differential Systems associated with Hopf bifurcation , 2013, Int. J. Bifurc. Chaos.

[14]  Pei Yu,et al.  Symbolic computation of limit cycles associated with Hilbert’s 16th problem , 2009 .

[15]  Pei Yu,et al.  COMPUTATION OF NORMAL FORMS VIA A PERTURBATION TECHNIQUE , 1998 .

[16]  Pei Yu,et al.  Four Limit cycles from perturbing quadratic integrable Systems by quadratic polynomials , 2012, Int. J. Bifurc. Chaos.

[17]  On a Żołądek theorem , 2008 .

[18]  Songling Shi,et al.  A CONCRETE EXAMPLE OF THE EXISTENCE OF FOUR LIMIT CYCLES FOR PLANE QUADRATIC SYSTEMS , 1980 .

[19]  H. Zoladek,et al.  Eleven small limit cycles in a cubic vector field , 1995 .

[20]  Chengzhi Li,et al.  A cubic system with thirteen limit cycles , 2009 .

[21]  Jibin Li,et al.  Hilbert's 16th Problem and bifurcations of Planar Polynomial Vector Fields , 2003, Int. J. Bifurc. Chaos.

[22]  Lindi M. Wahl,et al.  Viral Blips May Not Need a Trigger: How Transient Viremia Can Arise in Deterministic In-Host Models , 2014, SIAM Rev..

[23]  Yirong Liu,et al.  New Results on the Study of Zq-Equivariant Planar Polynomial Vector Fields , 2010 .

[24]  Shi Songling,et al.  On the structure of Poincaré-Lyapunov constants for the weak focus of polynomial vector fields , 1984 .

[25]  Yun Tian,et al.  Seven Limit Cycles Around a Focus Point in a Simple Three-Dimensional Quadratic Vector Field , 2014, Int. J. Bifurc. Chaos.

[26]  Valery G. Romanovski,et al.  Centers and limit cycles in polynomial systems of ordinary differential equations , 2016 .

[27]  Nikolay V. Kuznetsov,et al.  Visualization of Four Normal Size Limit Cycles in Two-Dimensional Polynomial Quadratic System , 2013 .