Estimation of the dimension of chaotic dynamical systems using neural networks and robust location estimate

In this paper, we propose a new algorithm for the estimation of the dimension of chaotic dynamical systems using neural networks and robust location estimate. The basic idea is that a member of a time series can be optimally expressed as a deterministic function of the d past series values, where d is the dimension of the system. Moreover the neural networks' learning ability is improved rapidly when the appropriate amount of information is provided to a neural structure which is as complex as needed. To estimate the dimension of a dynamical system, neural networks are trained to learn the component of the attractor expressed by a reconstructed vector in a suitable phase space whose embedding dimension m, has been estimated using the method of mutual information.