Functional consequences of model complexity in rhythmic systems: I. Systematic reduction of a bursting neuron model

Neural models are increasingly being used as design components of physical systems. In order to most effectively utilize neuronal models in these novel contexts, we need to develop design rules for neuronal systems that relate how model design affects overall system performance. In this paper and a companion article, we investigate how the complexity of a neural model affects the performance of a two-cell oscillator built from the model. In this paper, we create a series of related neuron models with different mathematical complexity. Starting with a complex mechanistic model of a bursting neuron, we use a variety of techniques to create a series of simplified neuron models. These three reduced models produce bursting activity that is qualitatively very similar to the original model. In the following companion article, we investigate the functional performance of oscillators built from these models.