Mathematical Models for Computational Neuroscience

We present the main aspects of mathematical models for computational neuroscience, with emphasis on the basic principles that can drive the construction of biologically inspired neural networks oriented to cognitive neuroscience problems. This chapter is subdivided into two distinct parts. In the first, the principal models of individual neural units (Hodgkin-Huxley, integrate and fire, and rate models) are described, together with a brief portrayal of synapse formalism. In the second, assuming rate models for simplicity, we summarize the peculiarities of important neural network typologies: associative networks (both hetero- and auto-association), self-organized networks, and error-correction networks (within the paradigm of reinforcement learning). For each network, simulation exempla are displayed and connections with physiological and pathological conditions of cognitive relevance are discussed. © 2014 Elsevier Inc. All rights reserved.