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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 τw = (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 τw is more crucial for the quality of reconstruction...
We propose an approach to computing two-dimensional unstable and stable manifolds of three-dimensional vector fields. The main idea is to estimate normal direction on each point around the boundary of current loop of manifold and normalize the normal growth rate during a settled time step to counter the disequilibrium in different directions. In order to enhance the reliability of our approach, linear...
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