For the planar Z2-equivariant cubic systems having twoelementary focuses, the characterization of a bi-center problem and shortened expressions of the first six Liapunov constants are completely discussed. The necessa...For the planar Z2-equivariant cubic systems having twoelementary focuses, the characterization of a bi-center problem and shortened expressions of the first six Liapunov constants are completely discussed. The necessary and sufficient conditions for the existence of the bi-center are obtained. All possible first integrals are given. Under small Z2-equivariant cubic perturbations, the conclusion that there exist at most 12 small-amplitude limit cycles with the scheme （6 II 6） is proved.展开更多
This paper considers two dimensional systems which have purely imaginary eigenvalues.In order to obtain more propositions of invariant curves,the authors transform the real systems into complex differential systems by...This paper considers two dimensional systems which have purely imaginary eigenvalues.In order to obtain more propositions of invariant curves,the authors transform the real systems into complex differential systems by using a suitable linear transformation.The authors also propose an algorithm to compute exponential factors.An improved method of constructing integrating factor by using all invariant curves is presented and can be used in determining the type of the equilibrium points.展开更多
In this paper we give a parallel algorithm for obtaining the eigenvalues and eigenvectors of a matrix.The practical background of this algorithm is the numerical computation in conjunction with the symbolic computation.
基金Supported by National Natural Science Foundation of China （Grant Nos. 10831003 and 10771196）
文摘For the planar Z2-equivariant cubic systems having twoelementary focuses, the characterization of a bi-center problem and shortened expressions of the first six Liapunov constants are completely discussed. The necessary and sufficient conditions for the existence of the bi-center are obtained. All possible first integrals are given. Under small Z2-equivariant cubic perturbations, the conclusion that there exist at most 12 small-amplitude limit cycles with the scheme （6 II 6） is proved.
基金supported by the National Natural Science Foundation of China under Grant No.11271363
文摘This paper considers two dimensional systems which have purely imaginary eigenvalues.In order to obtain more propositions of invariant curves,the authors transform the real systems into complex differential systems by using a suitable linear transformation.The authors also propose an algorithm to compute exponential factors.An improved method of constructing integrating factor by using all invariant curves is presented and can be used in determining the type of the equilibrium points.
文摘In this paper we give a parallel algorithm for obtaining the eigenvalues and eigenvectors of a matrix.The practical background of this algorithm is the numerical computation in conjunction with the symbolic computation.
