NDLI: Generation of Oscillatory Trajectories with Specified Stability Degree Using Recurrent Neural Networks

Content Provider	IEEE Xplore Digital Library
Author	Kuroe, Y. Miura, K.
Copyright Year	2006
Description	Author affiliation: Member, IEEE, Center for Information Science, Kyoto Institute of Technology, Matsugasaki, Sakyo-ku, Kyoto 606-8585, Japan. email: kuroe@kit.ac.jp (Kuroe, Y.)
Abstract	In the biological systems there are numerous examples of autonomously generated periodic activities. Several different periodic patterns are generated simultaneously in a living body. This paper discusses a method of generating periodic oscillatory trajectories in an artificial neural network. We propose a synthesis method of a neural network which generates desired autonomous periodic trajectories. The proposed method makes it possible to generate not only one periodic trajectory but also multiple different trajectories in a neural network simultaneously and to make each periodic trajectory possess specified stability degree. It is known that stability and stability degree of periodic trajectories (limit cycles) can be estimated by checking eigenvalues of Jacobian matrix of the Poincaré map defined on them. We propose a learning method of neural networks which makes the Poincaré map of each generated periodic trajectory possess specified stable eigenvalues. Experimental examples are presented to demonstrate the applicability and performance of the proposed method.
Starting Page	3478
Ending Page	3485
File Size	1427931
Page Count	8
File Format	PDF
ISBN	0780394909
DOI	10.1109/IJCNN.2006.247353
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2006-07-16
Publisher Place	Canada
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Stability Recurrent neural networks Artificial neural networks Trajectory Eigenvalues and eigenfunctions Biological systems Network synthesis Limit-cycles Jacobian matrices Learning systems
Content Type	Text
Resource Type	Article

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