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Analysis on equilibrium points of cellular neural networks with thresholding activation function

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Abstract

In previous paper, the number of equilibrium points of a cellular neural network (CNN) was studied. However, the region of different values of equilibrium points of every cell in the CNN is not investigated. Therefore, in this paper, the regions of the number of different values of equilibrium points in cellular neural networks (CNNs) with thresholding activation function are obtained by the relationship between parameters of CNNs. The influence of the values of connection weights of CNNs on the number of equilibrium points for a cell is found. Some sufficient conditions are obtained by using the relationship among connection weights. Depending on these sufficient conditions, inputs and outputs of a CNN, the regions of the values of parameters can be obtained. Finally, some numerical simulations are presented to support the effectiveness of the theoretical analysis.

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Acknowledgments

This work was supported in part by the National Natural Science Foundation of China under Grant 60973114, Grant 61170249 and Grant 61003247, in part by the Natural Science Foundation project of CQCSTC under Grant 2009BA2024, and in part by the State Key Laboratory of Power Transmission Equipment and System Security and New Technology, Chongqing University, under Grant 2007DA10512711206, in part by Teaching and Research Program of Chongqing Education Committee (KJ110401), in part by the First Batch of Supporting Program for University Excellent Talents in Chongqing, and in part by Research Project of Chongqing University of Science and Technology under Grant CK2011Z17.

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Authors and Affiliations

  1. School of Electrical and Information Engineering, Chongqing University of Science and Technology, Chongqing, 401331, China

    Qi Han, Tengfei Weng & Jun Peng

  2. State Key Laboratory of Power Transmission Equipment and System Security, College of Computer Science, Chongqing University, Chongqing, 400030, China

    Qi Han, Xiaofeng Liao, Chuandong Li & Liping Feng

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  1. Qi Han
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  2. Xiaofeng Liao
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  3. Tengfei Weng
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  4. Jun Peng
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  5. Chuandong Li
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  6. Liping Feng
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Correspondence to Qi Han.

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Han, Q., Liao, X., Weng, T. et al. Analysis on equilibrium points of cellular neural networks with thresholding activation function. Neural Comput & Applic 23, 23–29 (2013). https://doi.org/10.1007/s00521-012-1173-1

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  • DOI: https://doi.org/10.1007/s00521-012-1173-1

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