Abstract
In this paper, we show that a delayed discrete Hopfield neural network of two nonidentical neurons with no self-connections can demonstrate chaotic behavior in a region away from the origin. To this end, we first transform the model, by a novel way, into an equivalent system which enjoys some nice properties. Then, we identify a chaotic invariant set for this system and show that the system within this set is topologically conjugate to the full shift map on two symbols. This confirms chaos in the sense of Devaney. Our main result is complementary to the results in Kaslik and Balint (2008) and Huang and Zou (2005), where it was shown that chaos may occur in neighborhoods of the origin for the same system. We also present some numeric simulations to demonstrate our theoretical results.
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Chen, Y., Huang, Y. & Zou, X. Chaotic invariant sets of a delayed discrete neural network of two non-identical neurons. Sci. China Math. 56, 1869–1878 (2013). https://doi.org/10.1007/s11425-013-4640-y
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DOI: https://doi.org/10.1007/s11425-013-4640-y