An united algorithm for state space reconstruction

Traditionally embedding parameters: embedding dimension m and delay time τ are determined separately in state space reconstruction of chaotic dynamical systems. While recently some researchers argued that delay time window τ_w = (m-1)τ should be determined first. In this paper we carry out a contrast test and come to a conclusion that m rather than τ_w is more crucial for the quality of reconstruction. And according to the different impact of these parameters we put forward an united algorithm of FNN (False Nearest Neighbors) and AD (Average Displacement) methods to select m and τ. Finally we apply our method to Rössler system and get satisfactory results.