Computation of distinguished trajectories in time dependent vector fields

With definition of DHT (distinguished hyperbolic trajectory) and existing measure function in phase space, a measure function in extended phase space is presented. Existing algorithms with constant accuracy parameters is laborious as high precision is required. In order to overcome this shortage, a variable-step convergence algorithm is proposed. The main idea is to estimate initial region with the help of ISP (instantaneous stagnation points) and adopt variable-step grids to increase efficiency. With theoretical analysis and numerical calculation, an optimal range of key parameter is given. Two-dimensional and three-dimensional Duffing systems are used to test the performance. It shows that convergence route gained by the developed measure function is smooth and stable. And the variable-step convergence algorithm is more efficient.