A major challenge in neural network research is to build models that are simple enough for analysis but describe the biological behavior of the network and can be tested experimentally. Recent experimental and theoretical studies of small neural networks make the building of such models possible. In the proposed research we will build a detailed biological model of the pyloric Central Pattern Generator of the lobster. This model will be an extended version of the Hodgkin-Huxley model which includes the important currents and synaptic connections. Using methods from dynamical system theory and physical approximation we will obtain a simpler model which still describes the experimental results. A phase model will be developed from the full model. The effects of synaptic modification and changes of intrinsic properties of the neurons will be tested, and the effect of neurotransmitters will be investigated. The theoretical study will combine analytical and numerical methods from neural network and dynamical system theory, numerical simulations and will be compared to neurobiological experiments. The research will contribute to bridging the gap between regular neural network models and the biological reality.
