• Publications
  • Influence
Simulating, analyzing, and animating dynamical systems - a guide to XPPAUT for researchers and students
  • B. Ermentrout
  • Mathematics, Computer Science
  • Software, environments, tools
  • 2002
List of figures Preface 1. Installation 2 A Very Brief Tour of XPPAUT 3. Writing ODE Files for Differential Equations 4. XPPAUT in the Classroom 5. More Advanced Diffferential Equations 6. SpatialExpand
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Type I Membranes, Phase Resetting Curves, and Synchrony
TLDR
We use singular perturbation methods and averaging to show that this is a general property of Type I membrane models. Expand
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Inhibition-based rhythms: experimental and mathematical observations on network dynamics.
An increasingly large body of data exists which demonstrates that oscillations of frequency 12-80 Hz are a consequence of, or are inextricably linked to, the behaviour of inhibitory interneurons inExpand
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Neural networks as spatio-temporal pattern-forming systems
Models of neural networks are developed from a biological point of view. Small networks are analysed using techniques from dynamical systems. The behaviour of spatially and temporally organizedExpand
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Simulation of networks of spiking neurons: A review of tools and strategies
TLDR
We review different aspects of the simulation of spiking neural networks. Expand
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When inhibition not excitation synchronizes neural firing
TLDR
We show that if the rise time of the synapse is longer than the duration of an action potential, inhibition not excitation leads to synchronized firing. Expand
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Linearization of F-I Curves by Adaptation
  • B. Ermentrout
  • Mathematics, Medicine
  • Neural Computation
  • 1 October 1998
TLDR
We show that negative feedback to highly nonlinear frequency-current (F-I) curves results in an effective linearization. Expand
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On the human sensorimotor-cortex beta rhythm: Sources and modeling
TLDR
Cortical oscillations in the beta band (13-35 Hz) are known to be modulated by the GABAergic agonist benzodiazepine. Expand
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Spatially Structured Activity in Synaptically Coupled Neuronal Networks: I. Traveling Fronts and Pulses
TLDR
We consider traveling front and pulse solutions to a system of integro-differential equations used to describe the activity of synaptically coupled neuronal networks in a single spatial dimension. Expand
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The Effects of Spike Frequency Adaptation and Negative Feedback on the Synchronization of Neural Oscillators
TLDR
We study the role of adaptation in enhancing the synchronization properties of cortical neurons by studying the dynamics in the presence of adaptation and how this alters the response of the neural oscillation to inputs. Expand
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