Abstract

Present neural network models ignore temporal considerations, and hence synchronicity in neural networks, by representing neuron response with a transfer function relating frequency of action potentials (firing frequency) to activation potential. Models of living neuron based on the Hudgkin-Huxley model of the excitable membrane of the squid’s axon and its Fitzhugh-Nagumo approximation, exhibit much more complex and rich behavior than that described by firing frequency-activation potential models. We describe the theory, operation, and properties of an integrate-and-fire neuron which we call the bifurcating neuron and show it has rich complex behavior capable of exhibiting synchronous firing or phase-locked operation, periodic firing, chaotic firing, bursting, and bifurcation between these modes of operation. An optoelectronic realization of the bifurcating neuron in the form of a nonlinear relaxation oscillator is described and experimental verification of its behavior is presented. The circuit shows that bifurcating neuron networks could be easier to construct than sigmoidal neuron networks. A population of bifurcating neurons, coupled through a connection matrix, represent a bifurcating neural network that is expected to exhibit properties not normally observed in networks of sigmoidal neurons. These include feature binding, cognition, quenching, and chaos, all of which play a role in higher level brain function. We expect the bifurcating neuron will lead to a new generation of neural networks more neuromorphic and hence more powerful than networks being dealt with today and that optics will play a role in the implementation of bifurcating neuron networks.

© 1991 Optical Society of America