Deterministic and Stochastic Dynamics of Multi-variable Neuron Models: Resonance, Filtered Fluctuations and Sodium-current Inactivation

Neurons are the basic elements of the networks that constitute the computational units of the brain. They dynamically transform input information into sequences of electrical pulses. Therefore it is crucial to understand this transformation and identify simple neuron models which accurately reproduce the known features of biological neurons. This book addresses three different features of neurons. We start by exploring the effect of subthreshold resonance on the response of a periodically forced neuron and show qualitatively distinct responses including mode locking and chaos. Then we will consider an experimentally verified model with realistic spike-generating mechanism and study the effect of filtered synaptic fluctuations on the firing-rate response of the neuron. Finally, a model is studied that incorporates threshold variability of neurons. We determine the modulation of the input-output properties of the model due to oscillatory inputs and in the presence of synaptic fluctuations. This book would be useful to understand the above properties of neurons and to learn some mathematical methods in analyzing deterministic and stochastic neuron models.