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      1. 同濟橋梁講壇 2019年第27期
        發布時間:2019-11-26? ? ? ? 瀏覽次數:54



        報告標題:Computation and Visualization of Invariant Manifolds

        報告人:Zhikai Wang

        時間:11月28日  10:00-12:00


        主持人:趙林  教授


               In this talk, we start with the basic concepts of dynamical systems.  Then we introduce the general types of problems that the well-known software package AUTO solves.  AUTO uses a boundary value algorithm with Gaussian collocation and pseudo-arclength continuation.  The two features distinguish AUTO from other general ODE solvers for dynamical systems.  In order to compute 2D solution manifolds, AUTO uses orbit continuation.  With these tools, we study two famous problems, the Lorenz system and the circular restricted Three-Body problem (CR3BP). We briefly discuss the basic bifurcation and stability analysis  of  ODE  systems.  The  numerical  analysis  of  the  two  problems  leads  to  the  newest algorithm to compute the 2D stable manifold of the origin of the Lorenz system and the 2D unstable manifold of appropriate periodic orbits of the CR3BP. We utilize Python for the  flow  control  of  AUTO.  We  also  implement  two  visualization  packages,  QTPlaut  and MATPlaut.  They make possible the processing of large quantities of AUTO solution data with the OpenGL graphical library, dynamic memory allocation and interpolation methods.

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