GEOMETRIC DESCRIPTION AND COMPUTATIONAL METHOD FOR BIFURCATION

【摘要】 <正> In this paper, a vector field is constructed, and an equivalent relationship between inva-riant manifolds of the vector fields and solution manifolds of systems of nonlinear equa-tions is established. Consequently the study on the problem of solution bifurcation is turnedinto the study on the local behavior near the singular points of the vector field. This ap-proach is geometrically intuitive, providing a new numetical method for tracking the solu-ti on manifold and computing bifurcation.更多还原

【Abstract】 In this paper, a vector field is constructed, and an equivalent relationship between inva-riant manifolds of the vector fields and solution manifolds of systems of nonlinear equa-tions is established. Consequently the study on the problem of solution bifurcation is turnedinto the study on the local behavior near the singular points of the vector field. This ap-proach is geometrically intuitive, providing a new numetical method for tracking the solu-ti on manifold and computing bifurcation.更多还原