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The Bifurcating Neuron Network I
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DOI：10.1016/S0893-6080(00)00083-6.png)
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The Bifurcating Neuron (BN), a chaotic integrate-and-fire neuron, is a model of a neuron augmented by coherent modulation from its environment. The BN is mathematically equivalent to the sine-circle map, and this equivalence relationship allowed us to apply the mathematics of one-dimensional maps to the design of BN networks. The study of symmetry in the BN revealed that the BN can be configured to exhibit bistability that is controlled by attractor-merging crisis. Also, the symmetry of the bistability can be controlled by the introduction of a sinusoidal fluctuation to the threshold level of the BN. These two observations led us to the design of the BN Network 1 (BNN-1), a chaotic pulse-coupled neural network exhibiting associative memory. In numerical simulations, the BNN-1 showed a better performance than the continuous-time Hopfield network, as far as the spurious-minima problem is concerned and exhibited many biologically plausible characteristics. (C) 2001 Elsevier Science Ltd. All rights reserved.
Keyword:
bifurcating neuron
integrate-and-fire neuron
time coding
coherence
chaos
attractor-merging crisis
bifurcating neuron network
neural network
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