Bifurcation analysis for a discrete-time Hopfield neural network of two neurons with two delays and self-connections |
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Authors: | E. Kaslik St. Balint |
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Affiliation: | 1. Department of Mathematics, BITS Pilani, Pilani Campus, Rajasthan Pilani-333031, India;2. Centre for Ocean, Rivers, Atmosphere and Land Sciences, IIT Kharagpur 721302, India |
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Abstract: | In this paper, a bifurcation analysis is undertaken for a discrete-time Hopfield neural network of two neurons with two different delays and self-connections. Conditions ensuring the asymptotic stability of the null solution are found, with respect to two characteristic parameters of the system. It is shown that for certain values of these parameters, Fold or Neimark-Sacker bifurcations occur, but Flip and codimension 2 (Fold–Neimark-Sacker, double Neimark-Sacker, resonance 1:1 and Flip–Neimark-Sacker) bifurcations may also be present. The direction and the stability of the Neimark-Sacker bifurcations are investigated by applying the center manifold theorem and the normal form theory. |
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