Spiking neural network simulation: numerical integration with the Parker-Sochacki method |
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Authors: | Robert D Stewart Wyeth Bair |
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Institution: | (1) Department of Physiology, Anatomy and Genetics, University of Oxford, Oxford, OX1 3PT, UK |
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Abstract: | Mathematical neuronal models are normally expressed using differential equations. The Parker-Sochacki method is a new technique
for the numerical integration of differential equations applicable to many neuronal models. Using this method, the solution
order can be adapted according to the local conditions at each time step, enabling adaptive error control without changing
the integration timestep. The method has been limited to polynomial equations, but we present division and power operations
that expand its scope. We apply the Parker-Sochacki method to the Izhikevich ‘simple’ model and a Hodgkin-Huxley type neuron,
comparing the results with those obtained using the Runge-Kutta and Bulirsch-Stoer methods. Benchmark simulations demonstrate
an improved speed/accuracy trade-off for the method relative to these established techniques.
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Keywords: | Parker-Sochacki Spiking neural network Numerical integration Izhikevich Hodgkin-Huxley |
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