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Bifurcation Behavior for an Electronic Neural Network Model with Two Different Delays

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Abstract

In this paper, an electronic neural network model with two different delays is investigated. The conditions for the local stability and the existence of Hopf bifurcation at the equilibrium of the system are derived. By applying the normal form theory and center manifold theory, some explicit formulae for determining the stability and the direction of the Hopf bifurcation periodic solutions are obtained. Numerical simulations for justifying the theoretical analysis are also included. Finally, main conclusions are given.

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Acknowledgments

This work is supported by National Natural Science Foundation of China(No. 11261010, No. 11161015), Soft Science and Technology Program of Guizhou Province(No. 2011LKC2030), Natural Science and Technology Foundation of Guizhou Province(J[2012]2100), Governor Foundation of Guizhou Province([2012]53), Natural Science and Technology Foundation of Guizhou Province(2014), Natural Science Innovation Team Project of Guizhou Province ([2013]14) and Doctoral Foundation of Guizhou University of Finance and Economics (2010).

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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. Department of Mathematics and Physics, Guilin University of Technology, Guilin, 541004, People’s Republic of China

    Yuanfu Shao

  3. Department of Mathematics and Statistics, Henan University of Science and Technology, Luoyang, 471003, People’s Republic of China

    Peiluan Li

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  1. Changjin Xu
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  2. Yuanfu Shao
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  3. Peiluan Li
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Correspondence to Changjin Xu.

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Xu, C., Shao, Y. & Li, P. Bifurcation Behavior for an Electronic Neural Network Model with Two Different Delays. Neural Process Lett 42, 541–561 (2015). https://doi.org/10.1007/s11063-014-9372-7

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