Neural Fields, Stephen Coombes; Peter beim Graben; Roland Potthas

Автор: Stephen Coombes; Peter beim Graben; Roland Potthas
Название: Neural Fields
ISBN: 3662515113 ISBN-13(EAN): 9783662515112
Издательство: Springer
Рейтинг:
Цена: 93160.00 T
Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Neural field theory has a long-standing tradition in the mathematical and computational neurosciences. Beginning almost 50 years ago with seminal work by Griffiths and culminating in the 1970ties with the models of Wilson and Cowan, Nunez and Amari, this important research area experienced a renaissance during the 1990ties by the groups of Ermentrout, Robinson, Bressloff, Wright and Haken. Since then, much progress has been made in both, the development of mathematical and numerical techniques and in physiological refinement und understanding. In contrast to large-scale neural network models described by huge connectivity matrices that are computationally expensive in numerical simulations, neural field models described by connectivity kernels allow for analytical treatment by means of methods from functional analysis. Thus, a number of rigorous results on the existence of bump and wave solutions or on inverse kernel construction problems are nowadays available. Moreover, neural fields provide an important interface for the coupling of neural activity to experimentally observable data, such as the electroencephalogram (EEG) or functional magnetic resonance imaging (fMRI). And finally, neural fields over rather abstract feature spaces, also called dynamic fields, found successful applications in the cognitive sciences and in robotics. Up to now, research results in neural field theory have been disseminated across a number of distinct journals from mathematics, computational neuroscience, biophysics, cognitive science and others. There is no comprehensive collection of results or reviews available yet. With our proposed book Neural Field Theory, we aim at filling this gap in the market. We received consent from some of the leading scientists in the field, who are willing to write contributions for the book, among them are two of the founding-fathers of neural field theory: Shun-ichi Amari and Jack Cowan.

Автор: Guckenheimer John, Holmes Philip
Название: Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields
ISBN: 0387908196 ISBN-13(EAN): 9780387908199
Издательство: Springer
Рейтинг:
Цена: 121110.00 T
Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: From the reviews: "This book is concerned with the application of methods from dynamical systems and bifurcation theories to the study of nonlinear oscillations. Chapter 1 provides a review of basic results in the theory of dynamical systems, covering both ordinary differential equations and discrete mappings. Chapter 2 presents 4 examples from nonlinear oscillations. Chapter 3 contains a discussion of the methods of local bifurcation theory for flows and maps, including center manifolds and normal forms. Chapter 4 develops analytical methods of averaging and perturbation theory. Close analysis of geometrically defined two-dimensional maps with complicated invariant sets is discussed in chapter 5. Chapter 6 covers global homoclinic and heteroclinic bifurcations. The final chapter shows how the global bifurcations reappear in degenerate local bifurcations and ends with several more models of physical problems which display these behaviors." #Book Review - Engineering Societies Library, New York#1 "An attempt to make research tools concerning `strange attractors' developed in the last 20 years available to applied scientists and to make clear to research mathematicians the needs in applied works. Emphasis on geometric and topological solutions of differential equations. Applications mainly drawn from nonlinear oscillations." #American Mathematical Monthly#2

Автор: Adler
Название: Random Fields and Geometry
ISBN: 0387481125 ISBN-13(EAN): 9780387481128
Издательство: Springer
Рейтинг:
Цена: 93160.00 T
Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Divided into three parts, this book talks about the developments in the study of random fields. The first part tackles Gaussian processes, the second focuses on geometry, both integral and Riemannian and the third presents the geometry of excursion sets of random fields and the related - Euler characteristic approach - to extremal probabilities.

Автор: Robert Kozma; Walter J. Freeman
Название: Cognitive Phase Transitions in the Cerebral Cortex - Enhancing the Neuron Doctrine by Modeling Neural Fields
ISBN: 3319373528 ISBN-13(EAN): 9783319373522
Издательство: Springer
Рейтинг:
Цена: 95770.00 T
Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This intriguing book was born out of the many discussions the authors had in the past 10 years about the role of scale-free structure and dynamics in producing intelligent behavior in brains. The microscopic dynamics of neural networks is well described by the prevailing paradigm based in a narrow interpretation of the neuron doctrine.

Автор: Robert Kozma; Walter J. Freeman
Название: Cognitive Phase Transitions in the Cerebral Cortex - Enhancing the Neuron Doctrine by Modeling Neural Fields
ISBN: 3319244043 ISBN-13(EAN): 9783319244044
Издательство: Springer
Рейтинг:
Цена: 121890.00 T
Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This intriguing book was born out of the many discussions the authors had in the past 10 years about the role of scale-free structure and dynamics in producing intelligent behavior in brains. The microscopic dynamics of neural networks is well described by the prevailing paradigm based in a narrow interpretation of the neuron doctrine.