Note: Intro -- Preface -- The Neural Field: A Framework for Brain Data Integration? -- References -- Contents -- 1 Tutorial on Neural Field Theory -- 1.1 Background -- 1.1.1 Synaptic Processing -- 1.1.2 Dendritic Processing -- 1.2 Tissue Level Firing Rate Models with Axo-Dendritic Connections -- 1.2.1 Turing Instability Analysis -- 1.2.2 Weakly Nonlinear Analysis: Amplitude Equations -- 1.2.2.1 Amplitude Equations for Planar Neural Fields -- 1.2.3 Brain Wave Equations -- 1.3 Travelling Waves and Localised States -- 1.3.1 Travelling Front -- 1.3.2 Stationary Bump -- 1.3.3 Interface Dynamics -- 1.4 Inverse Neural Modelling -- 1.4.1 Inverse Problems -- 1.4.2 Cognitive Modelling -- Appendix 1 -- Appendix 2 -- Appendix 3 -- Appendix 4 -- References -- Part I Theory of Neural Fields -- 2 A Personal Account of the Development of the Field Theory of Large-Scale Brain Activity from 1945 Onward -- 2.1 Introduction -- 2.2 Lotka-Volterra Dynamics -- 2.2.1 A Neural Analogy -- 2.3 Population Dynamics -- 2.3.1 The Wilson-Cowan Equations -- 2.4 A Master Equation Approach -- 2.5 Field Theory -- 2.5.1 The Operator Map -- 2.5.2 Coherent States -- 2.5.3 Moment Generating Equations and Spin-Coherent States -- 2.5.4 A Neural Network Path Integral -- 2.6 Back to the Master Equation -- 2.6.1 A System-Size Expansion of the Master Equation -- 2.7 Another Look at Path Integrals -- 2.7.1 Bosonic Path-Integrals for Neural Networks -- 2.7.2 Observables of Neural Activity -- 2.7.3 The Effective Spiking Model -- 2.7.4 Variational Techniques -- 2.7.5 Renormalizing the Action -- 2.7.6 Avalanches -- 2.7.7 Calculations Concerning Brain Rhythms and Spike Statistics -- 2.7.8 Closed Moment Equations -- 2.8 Stochastic Wilson-Cowan Equations -- 2.8.1 The E/I Master Equation -- 2.8.2 Work in Progress -- 2.9 Concluding Remarks -- References. , 3 Heaviside World: Excitation and Self-Organization of Neural Fields -- 3.1 Introduction -- 3.2 Dynamics of Excitation in a Homogeneous Neural Field -- 3.2.1 1D 1-Layer Field -- 3.2.2 1D Field with Two Layers -- 3.2.3 2D Field of Neural Excitation -- 3.3 Self-Organization of Neural Fields -- 3.3.1 Field Model of Self-Organization -- 3.3.2 Dynamics of the Receptive Field -- 3.3.3 Equilibrium Solution of Learning -- 3.3.4 Stability of the Equilibrium Solution -- 3.3.5 Kohonen Map -- 3.4 Conclusions -- References -- 4 Spatiotemporal Pattern Formation in Neural Fields with Linear Adaptation -- 4.1 Introduction -- 4.2 Bifurcations from the Homogeneous State -- 4.2.1 One Spatial Dimension -- 4.2.1.1 Zero Eigenvalue -- 4.2.1.2 Imaginary Eigenvalues -- 4.2.2 Two Spatial Dimensions -- 4.2.2.1 Zero Eigenvalue -- 4.2.2.2 Imaginary Eigenvalues -- 4.2.3 Summary of Pattern Formation -- 4.3 Response to Inputs in the Ring Network -- 4.3.1 Existence of Stationary Bumps -- 4.3.2 Linear Stability of Stationary Bumps -- 4.3.3 Existence of Traveling Bumps -- 4.3.4 Linear Stability of Traveling Bumps -- 4.4 Activity Bumps on the Infinite Line -- 4.4.1 Natural and Stimulus-Induced Stationary Activity Bumps -- 4.4.2 Natural and Stimulus-Locked Traveling Activity Bumps -- References -- 5 PDE Methods for Two-Dimensional Neural Fields -- 5.1 Introduction -- 5.2 Results in One Spatial Dimension -- 5.3 Two Dimensional Bumps and Rings -- 5.4 Spiral Waves -- 5.5 Conclusion -- References -- 6 Numerical Simulation Scheme of One- and Two Dimensional Neural Fields Involving Space-Dependent Delays -- 6.1 Introduction -- 6.2 The Novel Principle -- 6.3 The Numerical Implementation in Two Spatial Dimensions -- 6.4 Conclusion -- References -- 7 Spots: Breathing, Drifting and Scattering in a Neural FieldModel -- 7.1 Introduction -- 7.2 Heaviside Firing Rate and Interface Dynamics. , 7.3 Equivalent PDE Model and Numerical Bifurcation Analysis -- 7.4 Amplitude Equations for Breathing -- 7.5 Drifting -- 7.6 Center Manifold Reduction: Particle Description -- 7.7 Scattering -- 7.8 Discussion -- Appendix -- References -- 8 Heterogeneous Connectivity in Neural Fields: A StochasticApproach -- 8.1 Introduction -- 8.2 Local Inhomogeneity in Connection Density -- 8.2.1 Travelling Fronts and Pulses -- 8.2.2 Persistent Fluctuations -- 8.2.2.1 Simple Deterministic Connection Function -- 8.2.3 Activity Patterns and Correlations -- 8.2.4 Persistent Fluctuations in 2D -- 8.3 Long Range Connections -- 8.4 Conclusions -- References -- 9 Stochastic Neural Field Theory -- 9.1 Introduction -- 9.2 Population Density Method and Mean Field Theory -- 9.3 Stochastic Rate-Based Models -- 9.3.1 Neural Langevin Equation -- 9.3.2 Neural Master Equation -- 9.3.3 Continuum Limit -- 9.4 Traveling Waves in Stochastic Neural Fields -- 9.4.1 Traveling Fronts in a Deterministic Neural Field -- 9.4.2 Stochastic Neural Field with Extrinsic Noise -- 9.4.3 Explicit Results for a Heaviside Rate Function -- 9.5 Path Integral Representation of a Stochastic Neural Field -- 9.5.1 Pulled Fronts, Absorbing States and Extinction Events -- 9.5.2 Derivation of Path Integral Representation -- 9.5.3 Hamiltonian-Jacobi Dynamics and Population Extinction in the Weak-Noise Limit -- References -- 10 On the Electrodynamics of Neural Networks -- 10.1 Introduction -- 10.2 Pyramidal Neuron Model -- 10.2.1 General Solution of the Circuit Equations -- 10.2.2 Observation Model -- 10.2.3 Neurodynamics -- 10.3 Leaky Integrate-and-Fire Model -- 10.3.1 Simplification -- 10.3.2 Simulation -- 10.4 Continuum Neural Field Model -- 10.4.1 Rate Model -- 10.4.2 Neuroelectrodynamics -- 10.5 Discussion -- References -- Part II Applications of Neural Fields -- 11 Universal Neural Field Computation. , 11.1 Introduction -- 11.2 Principles of Universal Computation -- 11.2.1 Variables and Data Types -- 11.2.2 Algorithms and Sequential Processes -- 11.3 Dynamic Field Automata -- 11.3.1 Turing Machines -- 11.3.2 Nonlinear Dynamical Automata -- 11.3.3 Neural Field Computation -- 11.4 Discussion -- References -- 12 A Neural Approach to Cognition Based on Dynamic Field Theory -- 12.1 Introduction -- 12.2 Grounding DFT in Neurophysiology -- 12.3 Dynamic Field Theory -- 12.4 DFT as an Approach to Cognition -- 12.5 Modeling Visual Working Memory and Change Detection with Dynamic Neural Fields -- 12.6 Conclusions -- References -- 13 A Dynamic Neural Field Approach to Natural and Efficient Human-Robot Collaboration -- 13.1 Introduction -- 13.2 Dynamic Neural Field Model of Joint Action -- 13.3 Model Details -- 13.4 Setup of Human-Robot Experiments -- 13.5 Results -- 13.5.1 Selection Based on an Anticipatory Model of Action Observation and Shared Task Knowledge -- 13.5.2 Understanding Partially Occluded Actions -- 13.6 Discussion -- References -- 14 Neural Field Modelling of the Electroencephalogram: Physiological Insights and Practical Applications -- 14.1 Introduction -- 14.2 A Mean Field Model of Electrocortical Rhythmogenesis -- 14.2.1 Model Extensions -- 14.3 Dynamical Features -- 14.3.1 A Novel Route to Chaos -- 14.3.2 Metabifurcations -- 14.3.3 Multistability -- 14.4 Physiological Relevance -- 14.4.1 The Resting Alpha Rhythm -- 14.4.1.1 Endogenous Pharmacological Modulation -- 14.4.1.2 Exogenous Pharmacological Modulation -- 14.4.2 Mass Action and the Monitoring of Anaesthetic Action -- 14.5 Conclusion -- References -- 15 Equilibrium and Nonequilibrium Phase Transitions in a Continuum Model of an Anesthetized Cortex -- 15.1 Introduction -- 15.2 Induction of Anesthesia as an Equilibrium Phase Transition. , 15.3 Critical Fluctuations at the ``Opalescent'' Point -- 15.4 Nonequilibrium Phase Transitions in the Cortical Model -- 15.4.1 Emergence of Hopf Instability -- 15.4.2 Emergence of Turing Instability -- 15.4.3 Mixed Modes: Hopf-Turing Interactions -- 15.5 Discussion -- 15.5.1 Critical Fluctuations -- 15.5.2 Nonequilibrium Phase Transitions in the Cortex -- 15.5.3 Effect of Anesthesia on Sub-brain Structures -- 15.5.4 Multiple Equilibria and Cortical Self-Organization -- Appendix -- Model Equations -- Modeling Propofol Anesthesia -- Linear Stability Analysis for Homogenous Stationary States -- References -- 16 Large Scale Brain Networks of Neural Fields -- 16.1 Introduction -- 16.2 Mathematical Formulation of a Large-Scale Brain Network of Neural Fields -- 16.3 Homogeneous Approximations of Neural Fields -- 16.4 Homogeneous Modeling of Neural Fields and First Heterogeneous Extensions -- 16.5 Full Brain Network Modeling Using the Connectome -- 16.6 The Virtual Brain -- 16.7 Conclusions and Final Remarks -- References -- 17 Neural Fields, Masses and Bayesian Modelling -- 17.1 Introduction -- 17.1.1 Neural Masses and Fields -- 17.1.2 Neural Fields as Models for Empirical Data -- 17.2 Generative Models for Cross Spectral Densities -- 17.2.1 The Jansen and Rit Model -- 17.2.2 The Canonical Microcircuit Model -- 17.2.3 Neural Field Extensions of the Canonical Microcircuit and Jansen-Rit Models -- 17.2.4 Power Spectra of Neural Fields -- 17.3 Neural Fields as Dynamic Causal Models -- 17.3.1 Probabilistic Models of Empirical Data and Their Inversion -- 17.3.2 LFP Auditory Cortex Data -- 17.3.3 MEG Data from the Visual Cortex -- 17.4 Conclusions -- References -- 18 Neural Field Dynamics and the Evolution of the Cerebral Cortex -- 18.1 Introduction -- 18.1.1 Genetic Expression, Cell Firing and Apoptosis in Cortical Development. , 18.1.2 Cell Firing and Synchronous Oscillation.

Note: Intro -- Contents -- Series Foreword -- Introduction -- 1 The Dynamical and Structural Basis of Brain Activity -- 1.1 Introduction -- 1.2 Attractors and Brain Dynamics -- 1.3 Autonomous Brain Dynamics -- 1.4 Conclusion -- 2 Functional Connectivity, Neurocognitive Networks, and Brain Dynamics -- 2.1 A Connectivity and Network Perspective on Cognition -- 2.2 Identifying Major Cognitive Networks -- 2.3 Intrinsic Connectivity Networks -- 2.4 Three Core Neurocognitive Networks -- 2.5 Dynamics of Signaling in the CEN, SN, and DMN -- 2.6 A Dynamical Network Model of Saliency, Attention, and Control -- 2.7 Conclusion -- 3 Decoding Mental States from Patterns of Brain Activity -- 3.1 Introduction -- 3.2 Multivariate Decoding -- 3.3 Decoding Dynamics -- 3.4 Conclusion -- 4 Transient Brain Dynamics -- 4.1 Transients versus Attractors in Perception -- 4.2 Robustness through Metastability: Winnerless Competition -- 4.3 Hierarchical Competition: Canonical Models -- 4.4 Modulation Instability and Resting-State Dynamics -- 4.5 Modeling Psychopathology -- 4.6 Conclusion -- 5 A Dynamic Field Account of Language-Related Brain Potentials -- 5.1 Introduction -- 5.2 ERP Experiment -- 5.3 Dynamic Cognitive Modeling -- 5.4 Conclusion -- 6 Recognition of Sequences of Sequences Using Nonlinear Dynamical Systems -- 6.1 Introduction -- 6.2 Stable Heteroclinic Channels -- 6.3 Hierarchies of Stable Heteroclinic Channels -- 6.4 Bayesian Recognition Using SHC Hierarchies -- 6.5 A Model of Speech Recognition -- 6.6 Some Simulated Examples -- 6.7 Discussion -- 7 The Stability of Information Flows in the Brain -- 7.1 How to Define an Information Flow in the Brain? -- 7.2 Working Memory Capacity -- 7.3 Limits of Sequential Language Processing -- 7.4 Interaction of Heteroclinic Channels: Binding Problem -- 7.5 Sequential Decision Making -- 7.6 Future Directions. , 8 Multiscale Electroencephalographic Dynamics and Brain Function -- 8.1 Neuronal Correlates of Electroencephalographic and Local Field Potential Rhythms -- 8.2 Measuring Multiscale Field Dynamics -- 8.3 Spatiotemporal Field Dynamics in Sleep -- 8.4 Mechanisms of Neuronal Synchronization -- 8.5 Effects of Electrical Fields on Neuronal Activity during Sleep -- 8.6 Conclusion -- 9 Mapping the Multiscale Information Content of Complex Brain Signals -- 9.1 Brain as a Complex System -- 9.2 Information-Theoretic Tools -- 9.3 Information and Nonlinear Dynamics -- 9.4 Approximate and Sample Entropy -- 9.5 Estimation of Sample Entropy -- 9.6 Multiscale Entropy -- 9.7 Applications of Multiscale Entropy -- 9.8 Complexity and Spectral Power -- 9.9 Complexity and Nonstationarity -- 9.10 Complexity and Network Structure -- 9.11 Conclusion -- 10 Connectivity and Dynamics of Neural Information Processing -- 10.1 Introduction -- 10.2 Structured Flows as Functional Units of Processes -- 10.3 Structured Flows on Manifolds -- 10.4 Emergence of SFMs from Spiking Neuron Networks -- 10.5 Functional Architectures: SFM and Timescale Hierarchies -- 10.6 Discussion -- 11 Transient Motor Behavior and Synchronization in the Cortex -- 11.1 Motor Behavior and Loss of Stability -- 11.2 Behavioral Models -- 11.3 A Model for Cortical Areas -- 11.4 Neural Mass Models - From Coupled Oscillators to Network Activity -- 11.5 Conclusion -- 12 Free Energy and Global Dynamics -- 12.1 Introduction -- 12.2 The Free-Energy Principle -- 12.3 Action and Its Observation -- 12.4 Conclusion -- 13 Perception, Action, and Utility: The Tangled Skein -- 13.1 Introduction -- 13.2 The Classical View -- 13.3 Segregation of Probability and Utility in the Brain? -- 13.4 Approximate Inference -- 13.5 New Vistas -- 13.6 Conclusion -- 14 Short Guide to Modern Nonlinear Dynamics -- 14.1 Dynamical Systems. , 14.2 Chaotic Dynamics -- 14.3 Homoclinic and Heteroclinic Dynamics -- 14.4 Conclusion -- Contributors -- Index.