Abstract and Applied Analysis
Volume 2013 (2013), Article ID 496217, 4 pages
Research Article

Neural Network Dynamics without Minimizing Energy

Department of Mathematics, National Taiwan Normal University, 88 Section 4, Ting Chou Road, Taipei 11677, Taiwan

Received 14 December 2012; Accepted 18 December 2012

Academic Editor: Jen-Chih Yao

Copyright © 2013 Mau-Hsiang Shih and Feng-Sheng Tsai. 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.


Content-addressable memory (CAM) has been described by collective dynamics of neural networks and computing with attractors (equilibrium states). Studies of such neural network systems are typically based on the aspect of energy minimization. However, when the complexity and the dimension of neural network systems go up, the use of energy functions might have its own limitations to study CAM. Recently, we have proposed the decirculation process in neural network dynamics, suggesting a step toward the reshaping of network structure and the control of neural dynamics without minimizing energy. Armed with the decirculation process, a sort of decirculating maps and its structural properties are built here, dedicated to showing that circulation breaking taking place in the connections among many assemblies of neurons can collaborate harmoniously toward the completion of network structure that generates CAM.