2015/08/29 by Pedro M. Lima, Lima, Pedro M., Evelyn Buckwar +1
Computer Science · Physics and Astronomy · #65M12 #65R20 #65Z05 #FOS: Mathematics #Model Reduction and Neural Networks #Neural Networks Stability and Synchronization #Neural Networks and Applications #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.1508.07484
openalex publication_date 2015/08/29 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28
We are concerned with the numerical solution of a class integro-differential\nequations, known as Neural Field Equations, which describe the large-scale\ndynamics of spatially structured networks of neurons. These equations have many\napplications in Neuroscience and Robotics. We describe a numerical method for\nthe approximation of solutions in the two-dimensional case, including a\nspace-dependent delay in the integrand function. Compared with known algorithms\nfor this type of equation we propose a scheme with higher accuracy in the time\ndiscretisation. Since computational efficiency is a key issue in this type of\ncalculations, we use a new method for reducing the complexity of the algorithm.\nThe convergence issues are discussed in detail and a number of numerical\nexamples is presented, which illustrate the performance of the method.\n