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Bifurcation Analysis for Simplified Five-Neuron Bidirectional Associative Memory Neural Networks with Four Delays

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Abstract

The paper deals with the stability and bifurcation analysis of a class of simplified five-neuron bidirectional associative memory neural networks with four delays. By discussing the characteristic transcendental equation and applying Hopf bifurcation theory, some sufficient conditions which guarantee the local stability and the existence of Hopf bifurcation of the neural networks are established. With the aid of the normal form theory and center manifold theory, we obtain some specific formulae to determine the stability and the direction of the Hopf bifurcation. Computer simulations are implemented to explain the key mathematical predictions. The paper ends with a brief conclusion.

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Correspondence to Changjin Xu.

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This work is supported by National Natural Science Foundation of China (No. 61673008) and Project of High-level Innovative Talents of Guizhou Province ([2016]5651) and Major Research Project of The Innovation Group of The Education Department of Guizhou Province ([2017]039), Project of Key Laboratory of Guizhou Province with Financial and Physical Features ([2017]004) and the Foundation of Science and Technology of Guizhou Province ([2018]1025 and [2018]1020).

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Xu, C., Liao, M., Li, P. et al. Bifurcation Analysis for Simplified Five-Neuron Bidirectional Associative Memory Neural Networks with Four Delays. Neural Process Lett 50, 2219–2245 (2019). https://doi.org/10.1007/s11063-019-10006-y

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