论文信息 - Symmetry in Planar Dynamical Systems

Symmetry in Planar Dynamical Systems

In the study of dynamical systems the conditions for a critical point to be a centre are often sought. The sufficiency of such conditions is probed using various techniques; here we exploit the possible symmetry of a given system. We describe an application of Grobner bases in the search for a bilinear transformation of the system to one which is symmetric in a line.

Noel G. Lloyd | Jane M. Pearson

[1] N. G. Lloyd,et al. Five limit cycles for a simple cubic system , 1997 .

[2] N G Lloyd,et al. Bifurcation of limit cycles and integrability of planar dynamical systems in complex form , 1999 .

[3] Dongming Wang,et al. Polynomial Systems from Certain Differential Equations , 1999, J. Symb. Comput..

[4] J. Guiver,et al. Multidimensional systems theory : progress, directions and open problems in multidimensional systems , 1985 .

[5] J. M. Pearson,et al. Computing centre conditions for certain cubic systems , 1992 .

[6] Dana Schlomiuk,et al. The centres in the reduced Kukles system , 1995 .

[7] N. Lloyd,et al. Transformation to Lienard form , 2000 .

[8] B. Buchberger,et al. Grobner Bases : An Algorithmic Method in Polynomial Ideal Theory , 1985 .

[9] Noel G. Lloyd,et al. REDUCE and the Bifurcation of Limit Cycles , 1990, J. Symb. Comput..

[10] Noel G. Lloyd,et al. Algorithmic Derivation of Centre Conditions , 1996, SIAM Rev..

[11] Noel G. Lloyd,et al. A cubic Kolmogorov system with six limit cycles , 2002 .