Torus Bifurcation Under Discretization  

作　　者：邹永魁 黄明游 

出　　处：《Northeastern Mathematical Journal》2002年第2期151-166,共16页东北数学（英文版）

基　　金：The NSFC (10071030) of China;The Volkswagen Foundation of Germany; The Project-sponsored by SRP for ROCS, SEM (2002).

摘　　要：Parameterized dynamical systems with a simple zero eigenvalue and a couple of purely imaginary eigenvalues are considered. It is proved that this type of eigen-structure leads to torus bifurcation under certain nondegenerate conditions. We show that the discrete systems, obtained by discretizing the ODEs using symmetric, eigen-structure preserving schemes, inherit the similar torus bifurcation properties. Predholm theory in Banach spaces is applied to obtain the global torus bifurcation. Our results complement those on the study of discretization effects of global bifurcation.Parameterized dynamical systems with a simple zero eigenvalue and a couple of purely imaginary eigenvalues are considered. It is proved that this type of eigen-structure leads to torus bifurcation under certain nondegenerate conditions. We show that the discrete systems, obtained by discretizing the ODEs using symmetric, eigen-structure preserving schemes, inherit the similar torus bifurcation properties. Predholm theory in Banach spaces is applied to obtain the global torus bifurcation. Our results complement those on the study of discretization effects of global bifurcation.

关 键 词：torus bifurcation symmetric scheme eigen-structure preserving scheme 

分 类 号：O241.81[理学—计算数学]