Numerical Investigation of Stochastic Neural Field Equations
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We introduce a new numerical algorithm for solving the stochastic neural field equation (NFE) with delays. Using this algorithm, we have obtained some numerical results which illustrate the effect of noise in the dynamical behaviour of stationary solutions of the NFE, in the presence of spatially heterogeneous external inputs.
We acknowledge support from Fundação para a Ciência e a Tecnologia (the Portuguese Foundation for Science and Technology) through the grant SFRH/BSAB/135130/2017 and POCI-01-0145-FEDER-031393.
- 5.Ferreira, F: Multi-bump solutions in dynamic neural fields: analysis and applications, PhD thesis, University of Minho, 2014. http://hdl.handle.net/1822/34416.
- 10.Hutt, A. and Rougier, N.: Numerical simulations of one- and two-dimensional neural fields involving space-dependent delays. In: S. Coombes et al. (Eds.), Neural Fields Theory and Applications, 175–183, Springer (2014).Google Scholar
- 15.Lima, P.M. and Buckwar, E.: Numerical investigation of the two-dimensional neural field equation with delay. In: Proceedings of the Second International Conference on Mathematics and Computers in Sciences and in Industry, 131–137, IEEE Conference Publications (2015).Google Scholar
- 19.Wolfram, S.: The Mathematica Book. Wolfram Media (2003).Google Scholar