{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,25]],"date-time":"2025-09-25T18:08:45Z","timestamp":1758823725055},"reference-count":18,"publisher":"MIT Press - Journals","issue":"9","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Neural Computation"],"published-print":{"date-parts":[[2003,9,1]]},"abstract":"<jats:p> A population density description of large populations of neurons has generated considerable interest recently. The evolution in time of the population density is determined by a partial differential equation (PDE). Most of the algorithms proposed to solve this PDE have used finite difference schemes. Here, I use the method of characteristics to reduce the PDE to a set of ordinary differential equations, which are easy to solve. The method is applied to leaky-integrate-and-fire neurons and produces an algorithm that is efficient and yields a stable and manifestly nonnegative density. Contrary to algorithms based directly on finite difference schemes, this algorithm is insensitive to large density gradients, which may occur during evolution of the density. <\/jats:p>","DOI":"10.1162\/089976603322297322","type":"journal-article","created":{"date-parts":[[2003,9,5]],"date-time":"2003-09-05T04:58:05Z","timestamp":1062737885000},"page":"2129-2146","source":"Crossref","is-referenced-by-count":28,"title":["A Simple and Stable Numerical Solution for the Population Density Equation"],"prefix":"10.1162","volume":"15","author":[{"given":"M. de","family":"Kamps","sequence":"first","affiliation":[{"name":"Section Cognitive Psychology, Faculty of Social Sciences, Leiden University, 2333 AK Leiden, The Netherlands,"}]}],"member":"281","reference":[{"key":"p_1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.48.1483"},{"key":"p_2","doi-asserted-by":"publisher","DOI":"10.1088\/0954-898X\/2\/3\/003"},{"key":"p_3","doi-asserted-by":"publisher","DOI":"10.1162\/089976602753633349"},{"key":"p_5","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.51.738"},{"key":"p_6","doi-asserted-by":"publisher","DOI":"10.1016\/S0893-6080(01)00053-3"},{"key":"p_7","doi-asserted-by":"publisher","DOI":"10.1088\/0954-898X\/3\/2\/004"},{"key":"p_8","doi-asserted-by":"publisher","DOI":"10.1088\/0954-898X\/12\/2\/304"},{"key":"p_11","doi-asserted-by":"publisher","DOI":"10.1016\/S0893-6080(01)00068-5"},{"key":"p_12","doi-asserted-by":"publisher","DOI":"10.1162\/089976600300015673"},{"key":"p_14","doi-asserted-by":"publisher","DOI":"10.1162\/089976600300015493"},{"key":"p_15","doi-asserted-by":"publisher","DOI":"10.1016\/0167-2789(91)90075-K"},{"key":"p_16","doi-asserted-by":"publisher","DOI":"10.1162\/neco.1997.9.2.279"},{"key":"p_17","doi-asserted-by":"publisher","DOI":"10.1023\/A:1008912914816"},{"key":"p_18","doi-asserted-by":"publisher","DOI":"10.1023\/A:1008964915724"},{"key":"p_19","doi-asserted-by":"publisher","DOI":"10.1088\/0954-898X\/14\/2\/305"},{"key":"p_20","doi-asserted-by":"publisher","DOI":"10.1137\/S0036139998344921"},{"key":"p_21","doi-asserted-by":"publisher","DOI":"10.1016\/S0006-3495(65)86709-1"},{"key":"p_22","doi-asserted-by":"publisher","DOI":"10.1007\/BF00335237"}],"container-title":["Neural Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mitpressjournals.org\/doi\/pdf\/10.1162\/089976603322297322","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,3,12]],"date-time":"2021-03-12T21:50:08Z","timestamp":1615585808000},"score":1,"resource":{"primary":{"URL":"https:\/\/direct.mit.edu\/neco\/article\/15\/9\/2129-2146\/6763"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,9,1]]},"references-count":18,"journal-issue":{"issue":"9","published-print":{"date-parts":[[2003,9,1]]}},"alternative-id":["10.1162\/089976603322297322"],"URL":"https:\/\/doi.org\/10.1162\/089976603322297322","relation":{},"ISSN":["0899-7667","1530-888X"],"issn-type":[{"value":"0899-7667","type":"print"},{"value":"1530-888X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2003,9,1]]}}}