The Bifurcating Neuron network 1.

G Lee; N H Farhat

doi:10.1016/s0893-6080(00)00083-6

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The Bifurcating Neuron network 1.

G Lee·N H Farhat

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Abstract

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.

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Action Potentials Brain Models, Neurological Neural Networks, Computer Neurons Nonlinear Dynamics Journal Article Research Support, U.S. Gov't, Non-P.H.S.

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G Lee, N H Farhat. 2001. The Bifurcating Neuron network 1.. https://doi.org/10.1016/s0893-6080(00)00083-6

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