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Chaotic invariant sets of a delayed discrete neural network of two non-identical neurons 被引量:6

Chaotic invariant sets of a delayed discrete neural network of two non-identical neurons
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摘要 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. 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.
出处 《Science China Mathematics》 SCIE 2013年第9期1869-1878,共10页 中国科学:数学(英文版)
基金 National Natural Science Foundation of China (Grant Nos. 11071263 and 11201504) the Natural Sciences and Engineering Research Council of Canada (Grant No. 227048-2010)
关键词 neural network Devaney chaos DISCRETE-TIME topological conjugacy 离散神经网络 不变集 神经元 离散Hopfield神经网络 混沌 延迟 等效系统 拓扑共轭
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