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arXiv · 1508.07484

Numerical Solution of the Neural Field Equation in the Two-dimensional Case

Pedro M. Lima·Evelyn Buckwar
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Abstract

We are concerned with the numerical solution of a class integro-differential equations, known as Neural Field Equations, which describe the large-scale dynamics of spatially structured networks of neurons. These equations have many applications in Neuroscience and Robotics. We describe a numerical method for the approximation of solutions in the two-dimensional case, including a space-dependent delay in the integrand function. Compared with known algorithms for this type of equation we propose a scheme with higher accuracy in the time discretisation. Since computational efficiency is a key issue in this type of calculations, we use a new method for reducing the complexity of the algorithm. The convergence issues are discussed in detail and a number of numerical examples is presented, which illustrate the performance of the method.

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Pedro M. Lima, Evelyn Buckwar. 2015-08-29. Numerical Solution of the Neural Field Equation in the Two-dimensional Case. https://arxiv.org/abs/1508.07484

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