Improving the performance of neural networks modeling strange attractors by the use of lvq neural networks as input signal controllers

Abstract

Back Propagation networks with Functional Link inputs can be used to satisfy the demand of structural uniformity in models of some chaotic attractors. Two such neural networks, with similar structures, are presented in this paper. They are used as models of the logistic and Henon map attractors and their structure includes a single hidden layer and Functional link inputs. Two different strategies were applied during the training phase, namely single and multiple. In single training, the networks memorize the attractor for the whole input space of the map, while in multiple training, each network memorizes the attractor for one subinterval of the input space. A significant reduction of error level was observed in every submodel arising from the multiple training process. However, since chaotic systems are governed by topological transitivity, no such subsystem can work independently. For this reason, an LVQ controller was created for each team of submodels, to feed the proper network with the input signal All networks were tested on large parts of chaotic orbits. The presented results for each case include both the RMS error and the distribution of the absolute error over pre-chosen error levels.

Keywords:

• Neural net
• Back Propagation
• LVQ controller
• chaotic attractor

C.R. Categories:

• I.2.4
• I.6.1