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KIAM Preprint ¹ 17, Moscow, 1993
Authors: Izhikevich E.M., Malinetskii G. G.
A neural network with chaotic behavior
The chaotic neural network (NN) is introduced as a model of olfactory system. The network is an n–dimensional map depended upon a parameter λ. While the parameter value is high NN is equivalent to the Hopfield’s network. While the value is low there are great number of chaotic and regular attractors. There is certain attractor for each memorized image (familiar odor). While external input is absent NN is in chaotic state. During inhalation of familiar odor the attractor corresponded to this odor becomes stable. NN approaches the attractor after some transitional period which we call “thinking”. During inhalation of unfamiliar odor the network remains in chaotic state which corresponds to “I don’t know” state. During inhalation of mixture of familiar odors all attractors that correspond to these odors become stable. NN is able to recognize even very weak odor under the background of stronger ones. During the recognition of inadequate stimulus there is transition from high–dimensional chaotic attractor corresponded to dormant state to the low–dimensional chaotic attractor corresponded to the certain inhaled odor. This model can illustrate the transitions “chaos–order” and “chaos–chaos” seen in the olfactory system of mammals.
neural network, pattern recognition, chaos, olfactory bulb
Publication language: russian,  pages: 32
Research direction:
Mathematical modelling in actual problems of science and technics
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About authors:
  • Izhikevich E.M.
  • Malinetskii Georgii Gennadyevich, RAS