Analysis of neural excitability and oscillations
Methods in neuronal modeling
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Intelligent computing about complex dynamical systems
Selected papers presented at the third international conference on Expert systems for scientific computing
An introduction to symbolic dynamics and coding
An introduction to symbolic dynamics and coding
Reasoning about nonlinear system identification
Artificial Intelligence
Matplotlib: A 2D Graphics Environment
Computing in Science and Engineering
Giant squid-hidden canard: the 3D geometry of the Hodgkin–Huxley model
Biological Cybernetics
Biological Cybernetics - Special Issue: Quantitative Neuron Modeling
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This work presents a neuroinformatic method for deriving mechanistic descriptions of fine-structured neural activity. This is a new development in the computer-assisted analysis of dynamics in conductance-based models, which is illustrated using single compartment models of an action potential. A sequence of abstract, qualitative motifs is inferred from this analysis, forming a template that is independent of the specific equations from which they were abstracted. The template encodes the assumptions behind the model reduction steps used to derive the motifs, and so specifies quantitative information about their domains of validity. The template representation of a mechanism is converted to a hybrid dynamical system, which is simulated as a sequence of low-dimensional reduced models (in this example, phase plane models) with appropriate switching conditions taken from the motifs. We demonstrate the validity of the template on a detailed single neuron model of spiking taken from the literature, and show that the corresponding hybrid system simulation closely mimics the spiking dynamics of the full model.