| Description |
1 online resource (xvi, 401 pages) : illustrations |
| Contents |
Cover -- PREFACE -- CONTENTS -- PART I: BURSTING AT THE SINGLE CELL LEVEL -- CHAPTER 1 THE DEVELOPMENT OF THE HINDMARSH-ROSE MODEL FOR BURSTING -- 1.1. Introduction -- 1.2. Tail Current Reversal -- 1.3. The 1982 Model -- 1.4. The 1984 Model -- 1.5. Subthreshold Oscillations -- 1.6. A Bifurcation Theorem -- References -- CHAPTER 2 NEGATIVE CALCIUM FEEDBACK: THE ROAD FROM CHAY-KEIZER -- 2.1. Introduction -- 2.2. Before the Beginning -- 2.3. The Beginning -- 2.4. The Demise of K(Ca) -- 2.5. The Return of K(Ca): Help from the Endoplasmic Reticulum -- 2.6. Further Modifications to the Model -- 2.7. Discussion -- Acknowledgements -- References -- CHAPTER 3 AUTOREGULATION OF BURSTING OF AVP NEURONS OF THE RAT HYPOTHALAMUS -- 3.1. Introduction -- 3.2. Electrical Properties of AVP Cells -- 3.3. Mathematical Model -- 3.4. Firing Patterns -- 3.5. Burst Structure -- 3.6. The Role of Calcium -- 3.7. The Action of Dynorphin -- 3.8. The Bursting Mechanism -- 3.9. The Dynamics of Dynorphin -- 3.10. Analysis of Bursting -- 3.11. Discussion -- Acknowledgements -- References -- CHAPTER 4 BIFURCATIONS IN THE FAST DYNAMICS OF NEURONS: IMPLICATIONS FOR BURSTING -- 4.1. Introduction -- 4.2. A TWO Dimensional Model of Spiking Sodium Currents -- 4.3. Fast-Slow Analysis of Bursting -- 4.4. Discussion -- References -- CHAPTER 5 BURSTING IN 2-COMPARTMENT NEURONS: A CASE STUDY OF THE PINSKY-RINZEL MODEL -- 5.1. Introduction -- 5.2. The Pinsky-Rinzel Model -- 5.3. Dynamics of the Pinsky-Rinzel Model -- 5.4. Morris-Lecar Two-Compartment Models -- 5.5. Discussion -- Acknowledgments -- References -- CHAPTER 6 GHOSTBURSTING: THE ROLE OF ACTIVE DENDRITES IN ELECTROSENSORY PROCESSING -- 6.1. Introduction -- 6.2. Bursting Mechanism -- 6.3. Ghostburster Dynamics -- 6.4. Unique Features -- 6.5. Extensions and Other Work -- 6.6. Parallel Processing with Bursts and Isolated Spikes -- 6.7. Summary -- Acknowledgements -- References -- PART II: BURSTING AT THE NETWORK LEVEL -- CHAPTER 7 ANALYSIS OF CIRCUITS CONTAINING BURSTING NEURONS USING PHASE RESETTING CURVES -- 7.1. Introduction -- 7.2. Stability Analysis for Two Coupled Oscillators -- 7.3. Analysis of a Circuit of Two Model Neurons -- 7.4. Stability Analysis for a Three Neuron Ring Circuit -- 7.5. Analysis of a Circuit of Three Model Neurons -- 7.6. Analysis of a Two Neuron Hybrid Circuit -- 7.7. Effect of Changing Burst Durations in the Two Neuron Circuit -- 7.8. Phenomenology of Resetting in a Biological Bursting Neuron -- 7.9. Significance -- Acknowledgments -- References -- CHAPTER 8 BURSTING IN COUPLED CELL SYSTEMS -- 8.1. Introduction -- 8.2. Unfolding Theory and Bursting in Fast-Slow Systems -- 8.3. Bursting in Two Coupled Cells -- 8.4. Za-Equivariant Bifurcations -- 8.5. Pitchfork Bifurcation -- 8.6. Hopf / Hopf Mode Interactions -- 8.7. Takens-Bogdanov Bifurcation with 22 Symmetry -- 8.8. Conclusion -- Acknowledgments -- References -- CHAPTER 9 MODULATORY EFFECTS OF COUPLING ON BURSTING MAPS -- 9.1. Introduction -- 9.2. Examples of Bursting Maps -- 9.3. Effects of Coupling -- 9.4. Rulkov's First Bursting Map: Explaining the Effect of Coupling -- 9.5. Discussion -- Acknowledgments -- References -- CHAPTER 10 BEYOND SYNCHRONIZATION: MODULAT |
| Summary |
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 |
| Bibliography |
Includes bibliographical references and index |
| Notes |
English |
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Print version record |
| Subject |
Neural transmission.
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Sensory neurons.
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Synaptic Transmission -- physiology
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Synaptic Transmission
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Neurons, Afferent -- physiology
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MEDICAL -- Neuroscience.
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PSYCHOLOGY -- Neuropsychology.
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Neural transmission
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Sensory neurons
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| Form |
Electronic book
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| Author |
Coombes, Stephen
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Bressloff, Paul C
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| ISBN |
9812703233 |
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9789812703231 |
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981256506X |
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9789812565068 |
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1281899208 |
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9781281899200 |
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9786611899202 |
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6611899200 |
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