
Using the CM method to control chaotic neural networks 
Revised:February 14, 2004 
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DOI：10.7511/jslx20062031 
KeyWord:CM(Contraction Mapping),chaos control,neural networks 
YU Hongjie PENG Jianhua LIU Yanzhu 

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Abstract: 
The CM(Contraction Mapping) method of chaos control based on contraction mappings is applied to discrete neural networks for stabilizing any unstable desired periodic orbit embedded in the chaotic attractor by a small external input.The close return pairs technique is utilized to estimate an approximate desired periodic orbit.The CM method utilizes only the approximate location of the desired periodic orbit,and does not require the linearization of the system around the stabilized orbit as required in OGY method.The desired periodic orbit can be detected automatically in control process.This approach is suitable for discrete neural networks of arbitrary dimension.To maintain the neural networks system onto the desired orbit,the necessary external input value is very small.Typical examples of neural networks are given,and the numerical simulations show validity and simplicity of the method for controlling the chaotic behavior of discrete neural networks. 