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On Chaotic Neural Network Design: A New Framework

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Abstract

The theory of chaos and chaotic neural networks (CNNs) has been widely investigated in the past two decades. However, most researchers in this area have merely focused on how to make full use of CNNs to solve various problems in areas such as pattern recognition, classification, associate memory and cryptography. The philosophy of how to design a CNN is seldom discussed. In this paper, we present a general methodology for designing CNNs. By appropriately choosing a self-feedback mechanism, and also including coupling functions and an external stimulus, we have succeeded in proving that a dynamical system, defined by discrete time feedback equations, does, indeed, possess interesting chaotic properties. To the best of our knowledge, the results presented here are novel and pioneering.

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Notes

  1. The authors of [6] also use this function and a modulus function to achieve the self-feedback.

  2. Please note that \({\varLambda }_{t}=\sigma (t)\cdot I\), and thus \({\varLambda }_{0}g'_0=g'_0{\varLambda }_{0}\).

  3. In this part of the paper, we only concentrate on the design of CNNs and we do not discuss their applications. This is why we randomly generate W and V here. However, W and V can be also weighted by appropriate learning algorithms for different applications.

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Acknowledgments

The author is extremely grateful to the anonymous Referees of the initial version of this paper for their valuable comments. Their comments significantly improved the quality of this paper. He is also sincerely grateful to Prof. B. J. Oommen from Carleton University in Canada, for being his friend and colleague, and for his valuable feedback. This work is supported by National Natural Science Foundation of China (Grant No. 61300093) and Fundamental Research Funds for the Central Universities in China (Grant No. ZYGX2013J071).

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  1. School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu, 611731, Sichuan, China

    Ke Qin

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Qin, K. On Chaotic Neural Network Design: A New Framework. Neural Process Lett 45, 243–261 (2017). https://doi.org/10.1007/s11063-016-9525-y

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