The Bifurcating Neuron network 1.
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.
Lee
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Electrical Engineering Department, University of Pennsylvania, Philadelphia 19104, USA.
Farhat
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D000200:Action Potentials / Q000502:physiology*; D001921:Brain / Q000502:physiology; D008959:Models, Neurological; D016571:Neural Networks, Computer; D009474:Neurons / Q000502:physiology*; D017711:Nonlinear Dynamics