The Numerical Computation Of Discrete Connecting Orbits On Manifold

In the field of scientific computing, the computation of connecting orbits on a manifold is relatively new area. With the rapid development of science and technology, the applications of dynamical systems on manifolds has made a great progress in many areas, for example, networks analysis, chemical engi-neering systems, ecosystems, optimum control, constrained mechanical system, etc. Compared with Euclidean space, the limitations of a manifold bring certain difficulties to study the dynamical systems on a manifold, and many results on Euclidean space can not be directly applied to the case on a manifold. In recent years, a large number of results about the stability analysis and numerical meth-ods of dynamical systems on a manifold have been obtained[5,6,7,8,13,12]. In this thesis, we introduce a numerical method to compute the connecting orbits of discrete dynamical systems on manifolds with. Numerical experiments are provided.We first briefly introduce some basic properties of continuous and discrete dynamical system on a manifold. Then we give a numerical approach to compute the connecting orbits of discrete dynamical systems on a manifold by introduc-ing a modified projection boundary condition. Finally, we study the numerical simulations of two models. The numerical results are provided.