The Bifurcating Neuron Network 2: an analog associative memory

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 a BN network. The study of the bifurcating diagram of the BN revealed that the BN, under a suitable condition, can function as an amplitude-to-phase converter. Also, being an integrate-and-fire neuron, it has an inherent capability to function as a coincidence detector. These two observations led us to the design of the BN Network 2 (BNN-2), a pulse-coupled neural network that exhibits associative memory of multiple analog patterns. In addition to the usual dynamical properties as an associative memory, the BNN-2 was shown to exhibit volume-holographic memory: it switches to different pages of its memory space as the frequency of the coherent modulation changes, meaning context-sensitive memory.