An improved algorithm for choosing delay time in phase space reconstruction

With embedding theorem proposed by Takens, we study methods for choosing proper delay time in phase space reconstruction of chaotic time series. A united method to incorporate advantages of average displacement and mutual information is put forward. In mutual information calculation we employ binary tree coding to divide and mark grids which makes it implemented easily. We determine layer numbers according to percentages of sparse grid. Numerical experiments of Rössler and Lorenz systems verifies accaracy of the method.