Hopf bifurcation analysis of a complex-valued neural network model with discrete and distributed delays

Li Li, Zhen Wang, Yuxia Li, Hao Shen and Junwei Lu

Applied Mathematics and Computation, 2018, vol. 330, issue C, 152-169

Abstract: In this paper, a class of complex-valued neural network model with discrete and distributed delays is proposed. Regarding the discrete time delay as the bifurcating parameter, the problem of Hopf bifurcation in the newly-proposed complex-valued neural network model is investigated under the assumption that the activation function can be separated into its real and imaginary parts. Based on the normal form theory and center manifold theorem, some sufficient conditions which determine the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are established. Finally, a numerical example is given to illustrate the validity of the theoretical results.

Keywords: Hopf bifurcation; Complex-valued; Neural network; Discrete delays; Distributed delays (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (22)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:330:y:2018:i:c:p:152-169

DOI: 10.1016/j.amc.2018.02.029

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