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Dynamics in Four-Neuron Bidirectional Associative Memory Networks with Inertia and Multiple Delays

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Abstract

Bidirectional associative memory (BAM) networks play an important role in various fields such as optimization, pattern recognition, classification, signal and image processing, parallel computation and associative memory. In this paper, four-neuron BAM networks with inertia and multiple delays are considered. By analyzing the distribution of the eigenvalues of the associated characteristic transcendental equation, local stability criteria are obtained for various system parameters and time delays. By choosing the sum of time delays as a bifurcation parameter, we found that Hopf bifurcation occurs when the sum of time delays passes through a sequence of critical values. Some explicit formulae for determining the stability and the direction of the Hopf bifurcation periodic solutions are obtained by using the normal form theory and center manifold theory. Some numerical simulations are carried out to support theoretical predictions. Our results are new and supplement some previously known studies.

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Acknowledgments

This work was supported by National Natural Science Foundation of China (Nos. 1126-1010, 11201138 and 11101126), Soft Science and Technology Program of Guizhou Province(No. 2011-LKC2030), Natural Science and Technology Foundation of Guizhou Province (J[2015]2025), Governor Foundation of Guizhou Province ([2012]53), Natural Science and Technology Foundation of Guizhou Province (2014), China Postdoctoral Science Foundation (No. 20110491249), Natural Science Innovation Team Project of Guizhou Province ([2013]14), Key Scientific and Technological Research Project of Department of Education of Henan Province (No. 12B110006), Youth Science Foundation of Henan University of Science and Technology (No. 2012QN010), Scientific Research Fund of Hunan Provincial Education Department (No. 12B034) and Natural Science Foundation to cultivating innovation ability of Henan University of Science and Technology (No. 2013ZCX020).

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Authors and Affiliations

  1. Guizhou Key Laboratory of Economics System Simulation, Guizhou University of Finance and Economics, Guiyang, 550004, People’s Republic of China

    Changjin Xu

  2. School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang, 471023, People’s Republic of China

    Peiluan Li

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  1. Changjin Xu
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Correspondence to Changjin Xu.

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Xu, C., Li, P. Dynamics in Four-Neuron Bidirectional Associative Memory Networks with Inertia and Multiple Delays. Cogn Comput 8, 78–104 (2016). https://doi.org/10.1007/s12559-015-9344-x

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