Table of Contents Author Guidelines Submit a Manuscript
Discrete Dynamics in Nature and Society
Volume 2014, Article ID 193758, 6 pages
Research Article

Levenberg-Marquardt Algorithm for Mackey-Glass Chaotic Time Series Prediction

1School of Mathematics, Liaocheng University, Liaocheng 252059, China
2School of Science, Huzhou University, Huzhou 313000, China
3School of Automation, Southeast University, Nanjing 210096, China

Received 9 August 2014; Accepted 11 October 2014; Published 11 November 2014

Academic Editor: Rongni Yang

Copyright © 2014 Junsheng Zhao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


For decades, Mackey-Glass chaotic time series prediction has attracted more and more attention. When the multilayer perceptron is used to predict the Mackey-Glass chaotic time series, what we should do is to minimize the loss function. As is well known, the convergence speed of the loss function is rapid in the beginning of the learning process, while the convergence speed is very slow when the parameter is near to the minimum point. In order to overcome these problems, we introduce the Levenberg-Marquardt algorithm (LMA). Firstly, a rough introduction is given to the multilayer perceptron, including the structure and the model approximation method. Secondly, we introduce the LMA and discuss how to implement the LMA. Lastly, an illustrative example is carried out to show the prediction efficiency of the LMA. Simulations show that the LMA can give more accurate prediction than the gradient descent method.