{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:57:20Z","timestamp":1760245040009},"reference-count":23,"publisher":"MIT Press - Journals","issue":"5","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Neural Computation"],"published-print":{"date-parts":[[2011,5]]},"abstract":"<jats:p> In traditional event-driven strategies, spike timings are analytically given or calculated with arbitrary precision (up to machine precision). Exact computation is possible only for simplified neuron models, mainly the leaky integrate-and-fire model. In a recent paper, Zheng, Tonnelier, and Martinez ( 2009 ) introduced an approximate event-driven strategy, named voltage stepping, that allows the generic simulation of nonlinear spiking neurons. Promising results were achieved in the simulation of single quadratic integrate-and-fire neurons. Here, we assess the performance of voltage stepping in network simulations by considering more complex neurons (quadratic integrate-and-fire neurons with adaptation) coupled with multiple synapses. To handle the discrete nature of synaptic interactions, we recast voltage stepping in a general framework, the discrete event system specification. The efficiency of the method is assessed through simulations and comparisons with a modified time-stepping scheme of the Runge-Kutta type. We demonstrated numerically that the original order of voltage stepping is preserved when simulating connected spiking neurons, independent of the network activity and connectivity. <\/jats:p>","DOI":"10.1162\/neco_a_00112","type":"journal-article","created":{"date-parts":[[2011,2,7]],"date-time":"2011-02-07T22:27:58Z","timestamp":1297117678000},"page":"1187-1204","source":"Crossref","is-referenced-by-count":5,"title":["On the Performance of Voltage Stepping for the Simulation of Adaptive, Nonlinear Integrate-and-Fire Neuronal Networks"],"prefix":"10.1162","volume":"23","author":[{"given":"Mohamed Ghaith","family":"Kaabi","sequence":"first","affiliation":[{"name":"Unit\u00e9 Mixte de Recherche 7503, LORIA, CNRS, 54506 Vandoeuvre-l\u00e8s-Nancy, France"}]},{"given":"Arnaud","family":"Tonnelier","sequence":"additional","affiliation":[{"name":"INRIA, 38334 Saint Ismier, France"}]},{"given":"Dominique","family":"Martinez","sequence":"additional","affiliation":[{"name":"Unit\u00e9 Mixte de Recherche 7503, LORIA, CNRS, 54506 Vandoeuvre-l\u00e8s-Nancy, France, and Unit\u00e9 Mixte de Recherche 1272, Physiologie de l'Insecte Signalisation et Communication, Institut National de la Recherche Agronomique, 78026 Versailles, France"}]}],"member":"281","reference":[{"key":"B1","doi-asserted-by":"publisher","DOI":"10.1162\/neco.2006.18.8.2004"},{"key":"B2","doi-asserted-by":"publisher","DOI":"10.1162\/neco.2007.19.10.2604"},{"key":"B3","doi-asserted-by":"publisher","DOI":"10.1152\/jn.00686.2005"},{"key":"B4","doi-asserted-by":"publisher","DOI":"10.1162\/neco.1996.8.5.979"},{"key":"B5","doi-asserted-by":"publisher","DOI":"10.1523\/JNEUROSCI.23-37-11628.2003"},{"key":"B6","doi-asserted-by":"publisher","DOI":"10.1126\/science.1181936"},{"key":"B7","first-page":"19","volume-title":"Proceedings of the 4th International Conference on Recent Advances in Soft Computing","author":"Girard A.","year":"2002"},{"key":"B8","volume-title":"5th International Workshop on Computer Algebra in Scientific Computing","author":"Girard A.","year":"2002"},{"key":"B9","doi-asserted-by":"publisher","DOI":"10.1162\/089976698300017845"},{"key":"B10","doi-asserted-by":"publisher","DOI":"10.1109\/TNN.2003.820440"},{"key":"B11","doi-asserted-by":"publisher","DOI":"10.1109\/TNN.2004.832719"},{"key":"B12","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.0712231105"},{"key":"B13","doi-asserted-by":"publisher","DOI":"10.1162\/089976600300014953"},{"key":"B14","doi-asserted-by":"publisher","DOI":"10.1007\/s10827-006-7949-5"},{"key":"B15","doi-asserted-by":"publisher","DOI":"10.1162\/neco.2007.19.1.47"},{"key":"B16","doi-asserted-by":"publisher","DOI":"10.1007\/s10827-006-8526-7"},{"key":"B17","volume-title":"In Proc. of the European Symposium on Artificial Neural Network","author":"Rochel O.","year":"2003"},{"key":"B18","doi-asserted-by":"publisher","DOI":"10.1023\/A:1012885314187"},{"key":"B19","doi-asserted-by":"publisher","DOI":"10.1162\/neco.2007.19.12.3226"},{"key":"B20","doi-asserted-by":"publisher","DOI":"10.1137\/070687268"},{"key":"B21","doi-asserted-by":"publisher","DOI":"10.1162\/neco.2009.09-08-853"},{"key":"B22","volume-title":"Theory of modeling and simulation","author":"Zeigler B. 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