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Journal of Inforamtion Science and Engineering, Vol.13 No.2, pp.293-310 (June 1997)
Sampling Effects on Trajectory Production and
Attractor Prediction*

Daw-Tung Lin
Computer Science Department
Chung-Hua Polytechnic Institute
30 Tung Shiang, Hsin Chu, Taiwan 30067

The time-delay neural network (TDNN) and the adaptive time-delay neural network (ATNN) are effective tools for signal production and trajectory generation. We present here the effects of different sampling rates on the production of trajectories by the ATNN neural network, including the influence of the sampling rate on the robustness and noise-resilience of the resulting system. Although fast training occurred with few samples per trajectory, and the trajectory was learned successfully, more resilience to noise was observed when there was a larger number of samples per trajectory. A major conclusion from these results is that the network learns the inherent features of the trajectory rather than memorizing each point. Although a large number of samples requires longer training, there are performance advantages in resilience to noise and in response to various start positions. The trained network generated intervening points on subsequent repetitions of the trajectory, a feature of limit cycle attractors observed in embedding dynamic networks. We show a relationship between the number of samples in the training set and network convergence speed of the ATNN on a chaotic series. The noise tolerance of the ATNN in chaotic series prediction is superior to that of the TDNN and is consistent with the divergence required for chaos to occur.

Keywords: sampling effect, adaptive time-delay neural network, trajectory learning, trajectory production, chaotic series prediction, attractor learning

Received August 7, 1996; revised December 2, 1996.
Communicated by Hsin-Chia Fu.
* This work was supported in part by the National Science Council (NSC 85-2213-E216-019), and the Applied Physics Laboratory of Johns Hopkins University. Author would like to thank Dr. Judith E. Dayhoff at the University of Maryland for her initialization for this work.