The Estimation of Periodic Solutions in Chaotic Time Series by Using Neural Networks

概要

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Chaos generated from nonlinear systems includes many periodic points and the estimation of these points is significant. In this paper, in order to estimate these periodic points, we formulate the optimal initial value decision problem for a nonlinear map at first. In the next, we consider the minimization function in this decision problem as a functional of the initial value, introduce the gradient of the functional by using a variational method, and present the method to solve the optimal initial value decision problem, when the fuction of a nonlinear map is given explicitly. In the third, we concerned with approximation of an unknown nonlinear map by using a neural network, and we estimates periodic points in the nonlinear map by using the neural network model. At last, we present the result of simulation by using the these methods.
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