Abstract
A simple two-neuron model of a discrete Hopfield neural network is considered. The local stability is analyzed with the associated characteristic model. In order to study the dynamic behavior, the Pitchfork bifurcation is examined. In the case of two neurons, one necessary condition for yielding the Pitchfork bifurcation is found. In addition, the stability and direction of the Pitchfork bifurcation are determined by applying the normal form theory and the center manifold theorem.
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Marichal, R., Piñeiro, J.D., González, E., Torres, J. (2010). Study of Pitchfork Bifurcation in Discrete Hopfield Neural Network. In: Ao, SI., Rieger, B., Amouzegar, M. (eds) Machine Learning and Systems Engineering. Lecture Notes in Electrical Engineering, vol 68. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-9419-3_10
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DOI: https://doi.org/10.1007/978-90-481-9419-3_10
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