Abstract
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1. Introduction
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2. One Dimensional Equations
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2.1. The Geometric Approach
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2.2. Bifurcations
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2.3. Bistability and Hysteresis
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3. Two Dimensional Systems
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3.1. The Phase Plane
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3.2. An Example
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3.3. Oscillations
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3.4. Local Bifurcations
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3.5. Global Bifurcations
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3.6. Geometric Singular Perturbation Theory
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4. Single Neurons
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4.1. Some Biology
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4.2. The Hodgkin-Huxley Equations
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4.3. Reduced Models
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4.4. Bursting Oscillations
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4.5. Traveling Wave Solutions
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5. Two Mutually Coupled Cells
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5.1. Introduction
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5.2. Synaptic Coupling
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5.3. Geometric Approach
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5.4. Synchrony with Excitatory Synapses
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5.5. Desynchrony with Inhibitory Synapses
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6. Activity Patterns in the Basal Ganglia
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6.1. Introduction
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6.2. The Basal Ganglia
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6.3. The Model
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6.4. Activity Patterns
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6.5. Concluding Remarks
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References
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© 2005 Springer-Verlag Berlin/Heidelberg
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Terman, D. (2005). An Introduction to Dynamical Systems and Neuronal Dynamics. In: Tutorials in Mathematical Biosciences I. Lecture Notes in Mathematics, vol 1860. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-31544-5_2
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DOI: https://doi.org/10.1007/978-3-540-31544-5_2
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Online ISBN: 978-3-540-31544-5
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