Nonlinear Brain Dynamics
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| Author | : Cornelis J. Stam |
| Publisher | : Nova Publishers |
| Total Pages | : 166 |
| Release | : 2006 |
| Genre | : Medical |
| ISBN | : 9781594548796 |
At the beginning of the 21st century, understanding the brain has become one of the final frontiers of science. Hailed as the 'most complex object in the universe' the brain still defies a complete understanding of its workings, in particular in relation to consciousness and higher brain functions. Despite enormous scientific efforts, the question how the 'mere matter' of 1011 interacting nerve cells can give rise to the inner world of our subjective feelings still remains an enigma. However, in contrast to a few decades ago, when respectable neuroscience was not expected to deal with such questions, the search for brain/mind relationships has now become the focus of intense research. The central idea of this book: to understand the brain, we need to understand its dynamics.
| Author | : Mikhail I. Rabinovich |
| Publisher | : MIT Press |
| Total Pages | : 371 |
| Release | : 2023-12-05 |
| Genre | : Medical |
| ISBN | : 0262549905 |
Experimental and theoretical approaches to global brain dynamics that draw on the latest research in the field. The consideration of time or dynamics is fundamental for all aspects of mental activity—perception, cognition, and emotion—because the main feature of brain activity is the continuous change of the underlying brain states even in a constant environment. The application of nonlinear dynamics to the study of brain activity began to flourish in the 1990s when combined with empirical observations from modern morphological and physiological observations. This book offers perspectives on brain dynamics that draw on the latest advances in research in the field. It includes contributions from both theoreticians and experimentalists, offering an eclectic treatment of fundamental issues. Topics addressed range from experimental and computational approaches to transient brain dynamics to the free-energy principle as a global brain theory. The book concludes with a short but rigorous guide to modern nonlinear dynamics and their application to neural dynamics.
| Author | : Eugene M. Izhikevich |
| Publisher | : MIT Press |
| Total Pages | : 459 |
| Release | : 2010-01-22 |
| Genre | : Medical |
| ISBN | : 0262514206 |
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.
| Author | : April A. Benasich |
| Publisher | : MIT Press |
| Total Pages | : 339 |
| Release | : 2022-06-07 |
| Genre | : Science |
| ISBN | : 0262545721 |
Experts explore the maturation of nonlinear brain dynamics from a developmental perspective and consider the relationship of neurodevelopmental disorders to early disruption in dynamic coordination. This volume in the Strüngmann Forum Reports series explores the complex mechanisms that accompany the dynamic processes by which the brain evolves and matures. Integrating perspectives from multiple disciplines, the book identifies knowledge gaps and proposes innovative ways forward for this emerging area of cross-disciplinary study. The contributors examine maturation of nonlinear brain dynamics across systems from a developmental perspective and relate these organizing networks to the establishment of normative cognition and pathology seen in many neurodevelopmental disorders. The book looks at key mechanistic questions, including: What role does dynamic coordination play in the establishment and maintenance of brain networks and structural and functional connectivity? How are local and global functional networks assembled and transformed over normative development? To what degree do oscillatory patterns vary across development? What is the impact of critical periods, and which factors initiate and terminate such periods? It also explores the potential of new technologies and techniques to enhance understanding of normative development and to enable early identification and remediation of neurodevelopmental and neuropsychiatric disorders that may result from early disruption in dynamic coordination. Contributors Sylvain Baillet, Yehezkel Ben-Ari, April A. Benasich, Olivier Bertrand, Gyorgy Buzsáki, Alain Chédotal, Sam M. Doesburg, Gordin Fishell, Adriana Galván, Jennifer N. Gelinas, Jay Giedd, Pierre Gressens, Ileana L. Hanganu-Opatz, Rowshanak Hashemiyoon, Takao K. Hensch, Suzana Herculano-Houzel, Mark Hübener, Mark, Matthias Kaschube, Michael S. Kobor, Bryan Kolb, Thorsten Kolling, Jean-Philippe Lachaux, Ulman Lindenberger, Heiko J. Luhmann, Hannah Monyer, Sarah R. Moore, Charles A. Nelson III, Tomáš Paus, Patrick L. Purdon, Pasko Rakic, Urs Ribary, Akira Sawa, Terrence J. Sejnowski, Wolf Singer, Cheryl L. Sisk, Nicholas C. Spitzer, Michael P. Stryker, Migranka Sur, Peter J. Uhlhaas
| Author | : Walter Freeman |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 395 |
| Release | : 2012-12-06 |
| Genre | : Medical |
| ISBN | : 1447103718 |
Cortical evoked potentials are of interest primarily as tests of changing neuronal excitabilities accompanying normal brain function. The first three steps in the anal ysis of these complex waveforms are proper placement of electrodes for recording, the proper choice of electrical or sensory stimulus parameters, and the establish ment of behavioral control. The fourth is development of techniques for reliable measurement. Measurement consists of comparison of an unknown entity with a set of standard scales or dimensions having numerical attributes in preassigned degree. A physical object can be described by the dimensions of size, mass, density, etc. In addition there are dimensions such as location, velocity, weight, hardness, etc. Some of these dimensions can be complex (e. g. size depends on three or more subsidiary coordi nates), and some can be interdependent or nonorthogonal (e. g. specification of size and mass may determine density). In each dimension the unit is defined with refer ence to a standard physical entity, e. g. a unit of mass or length, and the result of measurement is expressed as an equivalence between the unknown and the sum of a specified number of units of that entity. The dimensions of a complex waveform are elementary waveforms from which that waveform can be built by simple addition. Any finite single-valued function of time is admissible. They are called basis functions (lO, 15), and they can be expressed in numeric as well as geometric form.
| Author | : Hermann Haken |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 331 |
| Release | : 2007-12-22 |
| Genre | : Science |
| ISBN | : 3540752382 |
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.
| Author | : Wulfram Gerstner |
| Publisher | : Cambridge University Press |
| Total Pages | : 591 |
| Release | : 2014-07-24 |
| Genre | : Computers |
| ISBN | : 1107060834 |
This solid introduction uses the principles of physics and the tools of mathematics to approach fundamental questions of neuroscience.
| Author | : Raoul Huys |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 216 |
| Release | : 2010-12-08 |
| Genre | : Mathematics |
| ISBN | : 3642162614 |
Humans engage in a seemingly endless variety of different behaviors, of which some are found across species, while others are conceived of as typically human. Most generally, behavior comes about through the interplay of various constraints – informational, mechanical, neural, metabolic, and so on – operating at multiple scales in space and time. Over the years, consensus has grown in the research community that, rather than investigating behavior only from bottom up, it may be also well understood in terms of concepts and laws on the phenomenological level. Such top down approach is rooted in theories of synergetics and self-organization using tools from nonlinear dynamics. The present compendium brings together scientists from all over the world that have contributed to the development of their respective fields departing from this background. It provides an introduction to deterministic as well as stochastic dynamical systems and contains applications to motor control and coordination, visual perception and illusion, as well as auditory perception in the context of speech and music.
| Author | : J. A. Scott Kelso |
| Publisher | : MIT Press |
| Total Pages | : 368 |
| Release | : 1995 |
| Genre | : Medical |
| ISBN | : 9780262611312 |
foreword by Hermann Haken For the past twenty years Scott Kelso's research has focused on extending the physical concepts of self- organization and the mathematical tools of nonlinear dynamics to understand how human beings (and human brains) perceive, intend, learn, control, and coordinate complex behaviors. In this book Kelso proposes a new, general framework within which to connect brain, mind, and behavior.Kelso's prescription for mental life breaks dramatically with the classical computational approach that is still the operative framework for many newer psychological and neurophysiological studies. His core thesis is that the creation and evolution of patterned behavior at all levels--from neurons to mind--is governed by the generic processes of self-organization. Both human brain and behavior are shown to exhibit features of pattern-forming dynamical systems, including multistability, abrupt phase transitions, crises, and intermittency. Dynamic Patterns brings together different aspects of this approach to the study of human behavior, using simple experimental examples and illustrations to convey essential concepts, strategies, and methods, with a minimum of mathematics. Kelso begins with a general account of dynamic pattern formation. He then takes up behavior, focusing initially on identifying pattern-forming instabilities in human sensorimotor coordination. Moving back and forth between theory and experiment, he establishes the notion that the same pattern-forming mechanisms apply regardless of the component parts involved (parts of the body, parts of the nervous system, parts of society) and the medium through which the parts are coupled. Finally, employing the latest techniques to observe spatiotemporal patterns of brain activity, Kelso shows that the human brain is fundamentally a pattern forming dynamical system, poised on the brink of instability. Self-organization thus underlies the cooperative action of neurons that produces human behavior in all its forms.
| Author | : Erol Başar |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 186 |
| Release | : 2012-12-06 |
| Genre | : Medical |
| ISBN | : 3642755453 |
The analysis of deterministic chaos is currently an active field in many branches of research. Mathematically all nonlinear dynamical systems with more than two degrees of freedom can generate chaos, becoming unpredictable over a longer time scale. The brain is a nonlinear system par excellence. Accordingly, the concepts of chaotic dynamics have found, in the last five years, an important application in research on compound electrical activity of the brain. The present volume seeks to cover most of the relevant studies in the newly emerging field of chaotic attractors in the brain. This volume is essentially a selection and reorganization of contri butions from the first two volumes in the Springer Series in Brain Dynamics, which were based on conferences held in 1985 and 1987 in Berlin. It also includes (a) a survey of progress in the recording of evoked oscillations of the brain both at the cellular and EEG levels and (b) an agenda for research on chaotic dynamics. Although the first publications pointing out evidence of chaotic behavior of the EEG did not appear until the beginning of 1985, the presence of the pioneering scientists in this field gave the participants at the first conference (volume 1) a strong impulse toward this field. For me, as conference organizer, having been for a long time active in nonlinear EEG research, the integration of this topic was self-evident; however, the enthusiasm of the conference participants was greater than expected.
