Introduces the field of neuroscience that theoretically and experimentally studies how neurons work. In particular, the conductance-based model of Hodgkin-Huxley, its simplified version of FitzHugh-Nagumo and nonlinear integrate-and-fire models are discussed. Moreover, the dynamics of both neuronal populations and cognition are considered.
Neuronal Dynamics is a field of knowledge that creates models of individual neurons and biological neural networks of any part of the nervous system. Ongoing research efforts of spiking neural networks attempts to gain a better understanding of the brain and/or realize its electronic replicas that partially imitate brain functionalities such as learning and memory. In particular, the cortex is a complex system, characterized by its dynamics and architecture, which underlie many functions such as action, perception, learning, language, and cognition. Despite its structural architecture has been studied for more than a hundred years, its dynamics is not entirely understood.The book begins with a brief introduction that provides some basilar concepts about the neurophysiology of the neurons. In particular, the morphology of both neurons and synapsis, the action potentials and electrical properties of the cell membrane have been considered. Section 1 focuses on the most influential and enduring cellular model: the Hodgkin-Huxley action potential model, which historically was constructed for the squid giant axon and persists to this day. Section 2 discusses of integrate-and-fire neuron models which present the advantage to be well applicable to study the dynamics of large neuronal populations, due to their computational efficiency and analytical tractability. Section 3 present recent works about the FitzHugh-Nagumo model. In particular, the study of the influence of the cortex curvature on spreading depression, the propagation of excitation waves in moving media, and the identification of chaotic elements as a source of certain diseases have been taken into account. Section 4 deals with the interacting neuronal populations, the appearance of chaos in neuronal networks and the interaction between synaptic inhibition and glial-potassium dynamics. Finally, the last Section 5 focuses on dynamic of cognition. In particular, the key role of metastable states in the execution of cognitive functions, the statistical description of neuronal ensembles in terms of a Fokker-Planck equation, and the unification of probabilistic inference and synaptic plasticity by using a neuronal network that implements the well-studied Helmholtz Machine are discussed.
