Abstract

Typical Artificial Neural Network approaches to computation use processing elements which are combinatorial in nature, investing their computational properties in the pattern and strengths of the interconnections among them. While some aspects of nervous system function have been captured this way, other behaviors have remained obscure. Recently, techniques from nonlinear dynamics have been used to clarify the types and relationships among the complex behaviors exhibited by living neurons. This dissertation is motivated by the philosophy that the dynamics inherent in individual neurons is significant for their computational properties. Towards that end, techniques from the fields of point process mathematics and nonlinear dynamics are used to analyze information transfer across the unit of information processing in nervous systems, the synapse. This was accomplished by the development of an integrated computer environment for simulation, data analysis, and data visualization for models and data from a living preparations. The living preparation, the crayfish slowly adapting stretch receptor organ (SAO), is used for comparison with two different kinds of models. The first type of model is the leaky integrator, while the second is a more complex permeability-based one, inspired by the Hodgkin-Huxley model. Experiments on both the living preparation and the models involved periodic stimulation via an inhibitory synapse of the spontaneously firing pacemaker neuron (live or simulated). Results from the permeability model matched several complex behaviors of the SAO, and additionally directed examination of the SAO data in finding new behaviors. This is introduced as the initial stages of a much larger investigation that will explore successively more complex interactions across synaptic junctions and within networks.

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