Dynamical Systems in Neuroscience

Dynamical Systems in Neuroscience

In order to model neuronal behavior or to interpret the results of modeling studies, neuroscientists must call upon methods of nonlinear dynamics. This book offers an introduction to nonlinear dynamical systems theory for researchers and graduate students in neuroscience. It also provides an overview of neuroscience for mathematicians who want to learn the basic facts of electrophysiology. Dynamical Systems in Neuroscience presents a systematic study of the relationship of electrophysiology, nonlinear dynamics, and computational properties of neurons. It emphasizes that information processing in the brain depends not only on the electrophysiological properties of neurons but also on their dynamical properties. The book introduces dynamical systems, starting with one- and two-dimensional Hodgkin-Huxley-type models and continuing to a description of bursting systems. Each chapter proceeds from the simple to the complex, and provides sample problems at the end. The book explains all necessary mathematical concepts using geometrical intuition; it includes many figures and few equations, making it especially suitable for non-mathematicians. Each concept is presented in terms of both neuroscience and mathematics, providing a link between the two disciplines. Nonlinear dynamical systems theory is at the core of computational neuroscience research, but it is not a standard part of the graduate neuroscience curriculum—or taught by math or physics department in a way that is suitable for students of biology. This book offers neuroscience students and researchers a comprehensive account of concepts and methods increasingly used in computational neuroscience. An additional chapter on synchronization, with more advanced material, can be found at the author's website, www.izhikevich.com.

Nonlinear Dynamics in Computational Neuroscience

Nonlinear Dynamics in Computational Neuroscience

This book provides an essential overview of computational neuroscience. It addresses a broad range of aspects, from physiology to nonlinear dynamical approaches to understanding neural computation, and from the simulation of brain circuits to the development of engineering devices and platforms for neuromorphic computation. Written by leading experts in such diverse fields as neuroscience, physics, psychology, neural engineering, cognitive science and applied mathematics, the book reflects the remarkable advances that have been made in the field of computational neuroscience, an emerging discipline devoted to the study of brain functions in terms of the information-processing properties of the structures forming the nervous system. The content builds on the workshop “Nonlinear Dynamics in Computational Neuroscience: from Physics and Biology to ICT,” which was held in Torino, Italy in September 2015.

Stochastic Methods in Neuroscience

Stochastic Methods in Neuroscience

Computational or mathematical neuroscience is a research area currently of great interest, due to, amongst other factors, rapid increases in computing power, increases in the ability to record large amounts of neurophysiological data, and a realisation amongst both neuroscientists and mathematicians that each can benefit from collaborating with the other. This text will concentrate on the intersection between stochastic dynamics and neuroscience, presenting aseries of self-contained chapters on major aspects of noise and neuroscience, each written by an expert in their particular field. These range over Markov chain models for ion channel release, stochastically forced single neurons and population of neurons, statistical methods for parameter estimation,and the numerical approximation these models. Aimed at graduates and researchers in computational neuroscience and stochastic systems, each chapter will give an overview of a particular topic, including its history, important results in the area and future challenges.

The NEURON Book

The NEURON Book

The authoritative reference on NEURON, the simulation environment for modeling biological neurons and neural networks that enjoys wide use in the experimental and computational neuroscience communities. This book shows how to use NEURON to construct and apply empirically based models. Written primarily for neuroscience investigators, teachers, and students, it assumes no previous knowledge of computer programming or numerical methods. Readers with a background in the physical sciences or mathematics, who have some knowledge about brain cells and circuits and are interested in computational modeling, will also find it helpful. The NEURON Book covers material that ranges from the inner workings of this program, to practical considerations involved in specifying the anatomical and biophysical properties that are to be represented in models. It uses a problem-solving approach, with many working examples that readers can try for themselves.

Bursting

The Genesis of Rhythm in the Nervous System

Bursting

Neurons in the brain communicate with each other by transmitting sequences of electrical spikes or action potentials. One of the major challenges in neuroscience is to understand the basic physiological mechanisms underlying the complex spatiotemporal patterns of spiking activity observed during normal brain functioning, and to determine the origins of pathological dynamical states, such as epileptic seizures and Parkinsonian tremors. A second major challenge is to understand how the patterns of spiking activity provide a substrate for the encoding and transmission of information, that is, how do neurons compute with spikes? It is likely that an important element of both the dynamical and computational properties of neurons is that they can exhibit bursting, which is a relatively slow rhythmic alternation between an active phase of rapid spiking and a quiescent phase without spiking. This book provides a detailed overview of the current state-of-the-art in the mathematical and computational modelling of bursting, with contributions from many of the leading researchers in the field.

An Introductory Course in Computational Neuroscience

An Introductory Course in Computational Neuroscience

A textbook for students with limited background in mathematics and computer coding, emphasizing computer tutorials that guide readers in producing models of neural behavior. This introductory text teaches students to understand, simulate, and analyze the complex behaviors of individual neurons and brain circuits. It is built around computer tutorials that guide students in producing models of neural behavior, with the associated Matlab code freely available online. From these models students learn how individual neurons function and how, when connected, neurons cooperate in a circuit. The book demonstrates through simulated models how oscillations, multistability, post-stimulus rebounds, and chaos can arise within either single neurons or circuits, and it explores their roles in the brain. The book first presents essential background in neuroscience, physics, mathematics, and Matlab, with explanations illustrated by many example problems. Subsequent chapters cover the neuron and spike production; single spike trains and the underlying cognitive processes; conductance-based models; the simulation of synaptic connections; firing-rate models of large-scale circuit operation; dynamical systems and their components; synaptic plasticity; and techniques for analysis of neuron population datasets, including principal components analysis, hidden Markov modeling, and Bayesian decoding. Accessible to undergraduates in life sciences with limited background in mathematics and computer coding, the book can be used in a “flipped” or “inverted” teaching approach, with class time devoted to hands-on work on the computer tutorials. It can also be a resource for graduate students in the life sciences who wish to gain computing skills and a deeper knowledge of neural function and neural circuits.

A Dynamic Systems Approach to the Development of Cognition and Action

A Dynamic Systems Approach to the Development of Cognition and Action

"A radical departure from most of current cognitive development theory.... Nativists, structuralists, empiricists and social constructivists will disagree with different parts of this book. Yet this landmark volume is essential reading for all of them." -- Annette Karmiloff-Smith and Mark H. Johnson, "Nature" A Dynamic Systems Approach to the Development of Cognition and Action presents a comprehensive and detailed theory of early human development based on the principles of dynamic systems theory. Beginning with their own research in motor, perceptual, and cognitive development, Thelen and Smith raise fundamental questions about prevailing assumptions in the field. They propose a new theory of the development of cognition and action, unifying recent advances in dynamic systems theory with current research in neuroscience and neural development. In particular, they show how by processes of exploration and selection, multimodal experiences form the bases for self-organizing perception-action categories. Thelen and Smith offer a radical alternative to current cognitive theory, both in their emphasis on dynamic representation and in their focus on processes of change. Among the first attempt to apply complexity theory to psychology, they suggest reinterpretations of several classic issues in early cognitive development. The book is divided into three sections. The first discusses the nature of developmental processes in general terms, the second covers dynamic principles in process and mechanism, and the third looks at how a dynamic theory can be applied to enduring puzzles of development. Cognitive Psychology series

Mathematical Approaches to Biological Systems

Networks, Oscillations, and Collective Motions

Mathematical Approaches to Biological Systems

This book presents the most recent mathematical approaches to the growing research area of networks, oscillations, and collective motions in the context of biological systems. Bringing together the results of multiple studies of different biological systems, this book sheds light on the relations among these research themes. Included in this book are the following topics: feedback systems with time delay and threshold of sensing (dead zone), robustness of biological networks from the point of view of dynamical systems, the hardware-oriented neuron modeling approach, a universal mechanism governing the entrainment limit under weak forcing, the robustness mechanism of open complex systems, situation-dependent switching of the cues primarily relied on by foraging ants, and group chase and escape. Research on different biological systems is presented together, not separated by specializations or by model systems. Therefore, the book provides diverse perspectives at the forefront of current mathematical research on biological systems, especially focused on networks, oscillations, and collective motions. This work is aimed at advanced undergraduate, graduate, and postdoctoral students, as well as scientists and engineers. It will also be of great use for professionals in industries and service sectors owing to the applicability of topics such as networks and synchronizations.