An Introduction To Modeling Neuronal Dynamics
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An Introduction To Modeling Neuronal Dynamics
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Author : Christoph Börgers
language : en
Publisher: Springer
Release Date : 2017-04-17
An Introduction To Modeling Neuronal Dynamics written by Christoph Börgers and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-04-17 with Mathematics categories.
This book is intended as a text for a one-semester course on Mathematical and Computational Neuroscience for upper-level undergraduate and beginning graduate students of mathematics, the natural sciences, engineering, or computer science. An undergraduate introduction to differential equations is more than enough mathematical background. Only a slim, high school-level background in physics is assumed, and none in biology. Topics include models of individual nerve cells and their dynamics, models of networks of neurons coupled by synapses and gap junctions, origins and functions of population rhythms in neuronal networks, and models of synaptic plasticity. An extensive online collection of Matlab programs generating the figures accompanies the book.
Brain Dynamics
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Author : Hermann Haken
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-12-22
Brain Dynamics written by Hermann Haken and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-12-22 with Science categories.
This is an excellent introduction for graduate students and nonspecialists to the field of mathematical and computational neurosciences. The book approaches the subject via pulsed-coupled neural networks, which have at their core the lighthouse and integrate-and-fire models. These allow for highly flexible modeling of realistic synaptic activity, synchronization and spatio-temporal pattern formation. The more advanced pulse-averaged equations are discussed.
An Introduction To The Modeling Of Neural Networks
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Author : Pierre Peretto
language : en
Publisher: Cambridge University Press
Release Date : 1992-10-29
An Introduction To The Modeling Of Neural Networks written by Pierre Peretto and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-10-29 with Computers categories.
This book is a beginning graduate-level introduction to neural networks which is divided into four parts.
Neuronal Dynamics
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Author : Wulfram Gerstner
language : en
Publisher: Cambridge University Press
Release Date : 2014-07-24
Neuronal Dynamics written by Wulfram Gerstner and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-24 with Computers categories.
This solid introduction uses the principles of physics and the tools of mathematics to approach fundamental questions of neuroscience.
Introduction To Neural Dynamics And Signal Transmission Delay
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Author : Jianhong Wu
language : en
Publisher: Walter de Gruyter
Release Date : 2011-07-20
Introduction To Neural Dynamics And Signal Transmission Delay written by Jianhong Wu and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-07-20 with Mathematics categories.
In the design of a neural network, either for biological modeling, cognitive simulation, numerical computation or engineering applications, it is important to investigate the network's computational performance which is usually described by the long-term behaviors, called dynamics, of the model equations. The purpose of this book is to give an introduction to the mathematical modeling and analysis of networks of neurons from the viewpoint of dynamical systems.
Neuronal Dynamics
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Author : Stefano Spezia
language : en
Publisher: Arcler Press
Release Date : 2017-11
Neuronal Dynamics written by Stefano Spezia and has been published by Arcler Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11 with categories.
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.
Dynamical Systems In Neuroscience
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Author : Eugene M. Izhikevich
language : en
Publisher: MIT Press
Release Date : 2010-01-22
Dynamical Systems In Neuroscience written by Eugene M. Izhikevich and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-01-22 with Medical categories.
Explains the relationship of electrophysiology, nonlinear dynamics, and the computational properties of neurons, with each concept presented in terms of both neuroscience and mathematics and illustrated using geometrical intuition. 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.
Computational Neuroscience
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Author : Erik De Schutter
language : en
Publisher: CRC Press
Release Date : 2000-11-22
Computational Neuroscience written by Erik De Schutter and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-11-22 with Mathematics categories.
Designed primarily as an introduction to realistic modeling methods, Computational Neuroscience: Realistic Modeling for Experimentalists focuses on methodological approaches, selecting appropriate methods, and identifying potential pitfalls. The author addresses varying levels of complexity, from molecular interactions within single neurons to the
Methods In Neuronal Modeling
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Author : Christof Koch
language : en
Publisher: MIT Press
Release Date : 1998
Methods In Neuronal Modeling written by Christof Koch and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Nervous system categories.
Kinetic Models of Synaptic Transmission / Alain Destexhe, Zachary F. Mainen, Terrence J. Sejnowski / - Cable Theory for Dendritic Neurons / Wilfrid Rall, Hagai Agmon-Snir / - Compartmental Models of Complex Neurons / Idan Segev, Robert E. Burke / - Multiple Channels and Calcium Dynamics / Walter M. Yamada, Christof Koch, Paul R. Adams / - Modeling Active Dendritic Processes in Pyramidal Neurons / Zachary F. Mainen, Terrence J. Sejnowski / - Calcium Dynamics in Large Neuronal Models / Erik De Schutter, Paul Smolen / - Analysis of Neural Excitability and Oscillations / John Rinzel, Bard Ermentrout / - Design and Fabrication of Analog VLSI Neurons / Rodney Douglas, Misha Mahowald / - Principles of Spike Train Analysis / Fabrizio Gabbiani, Christof Koch / - Modeling Small Networks / Larry Abbott, Eve Marder / - Spatial and Temporal Processing in Central Auditory Networks / Shihab Shamma / - Simulating Large Networks of Neurons / Alexander D. Protopapas, Michael Vanier, James M. Bower / ...
Dynamical Systems In Neuroscience
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Author : Eugene M. Izhikevich
language : en
Publisher: MIT Press
Release Date : 2007
Dynamical Systems In Neuroscience written by Eugene M. Izhikevich and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Differentiable dynamical systems categories.
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.