Modeling chaotic behavior of discrete dynamical systems in two-dimension using Kohonen Som

• Main Author: Fortuna, Janice C.
• Format: text
• Language: English
• Published: Animo Repository 2004
• Subjects: Skidmore, Owings & Merrill; Architecture, Modern > 20th century; Mathematical models; Discrete-time systems; Chaotic behavior in systems; Computer Sciences
• Online Access: https://animorepository.dlsu.edu.ph/etd_masteral/3294; https://animorepository.dlsu.edu.ph/context/etd_masteral/article/10132/viewcontent/CDTG003908_P.pdf
• Institution: De La Salle University

The SOM architecture, training, and the self-organizing feature map is a popular neural network model adhering to the unsupervised learning paradigm and its being widely used for the cluster analysis of high dimensional data. This study investigates the capability of the Kohonen SOM to learn and model chaotic behavior of discrete dynamical system in two-dimension. The most central issues to adaptive self-organizing learning in a Kohonen network are the weight adaptation process and the concept of topological neighborhood of nodes. As it has been observed that the success of map formation is critically dependent on how the main parameters of the Kohonen learning algorithm, namely the learning rate parameter and the neighborhood function are selected. Since there is no theoretical basis for the selection of these parameters, they are usually determined by a process of trial and error. These parameters are selected with some underlying facts and issues in the Kohonen rule. This paper proposed a learning rate parameter function to improve the works of Welstead in modeling chaotic behavior of a Henon Map using Kohonen SOM learning algorithm. This study does not only improve the works of Welstead but also to model chaotic behavior of other discrete dynamical systems in two-dimension. Since this study focuses on the proposed learning rate parameter function, a neighborhood function for the Kohonen network algorithm is adopted. Two neighborhood functions are investigated and tested in this study. These are the static neighborhood function used by Welstead and compared it with a dynamic neighborhood function suggested by Dayhoff. Experiments are conducted and results are presented. Sample results of Welstead works are also presented and compared with the results in this study.