{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T13:13:24Z","timestamp":1753881204457,"version":"3.41.2"},"reference-count":17,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2012,12,25]],"date-time":"2012-12-25T00:00:00Z","timestamp":1356393600000},"content-version":"vor","delay-in-days":359,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11201084"],"award-info":[{"award-number":["11201084"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2012,1]]},"abstract":"<jats:p>This paper deals with the oscillations of numerical solutions for the nonlinear delay differential equations in physiological control systems. The exponential <jats:italic>\u03b8<\/jats:italic>\u2010method is applied to <jats:italic>p<\/jats:italic><jats:sup>\u2032<\/jats:sup>(<jats:italic>t<\/jats:italic>) = \u2009<jats:italic>\u03b2<\/jats:italic><jats:sub>0<\/jats:sub><jats:italic>\u03c9<\/jats:italic><jats:sup><jats:italic>\u03bc<\/jats:italic><\/jats:sup><jats:italic>p<\/jats:italic>(<jats:italic>t<\/jats:italic> \u2212 <jats:italic>\u03c4<\/jats:italic>)\/<jats:italic>(\u03c9<\/jats:italic><jats:sup><jats:italic>\u03bc<\/jats:italic><\/jats:sup> + <jats:italic>p<\/jats:italic><jats:sup><jats:italic>\u03bc<\/jats:italic><\/jats:sup>(<jats:italic>t<\/jats:italic> \u2212 <jats:italic>\u03c4<\/jats:italic>)) \u2212 <jats:italic>\u03b3<\/jats:italic><jats:italic>p<\/jats:italic>(<jats:italic>t<\/jats:italic>) and it is shown that the exponential <jats:italic>\u03b8<\/jats:italic>\u2010method has the same order of convergence as that of the classical <jats:italic>\u03b8<\/jats:italic>\u2010method. Several conditions under which the numerical solutions oscillate are derived. Moreover, it is proven that every nonoscillatory numerical solution tends to positive equilibrium of the continuous system. Finally, the main results are illustrated with numerical examples.<\/jats:p>","DOI":"10.1155\/2012\/348384","type":"journal-article","created":{"date-parts":[[2012,12,25]],"date-time":"2012-12-25T21:04:01Z","timestamp":1356469441000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Numerical Oscillations Analysis for Nonlinear Delay Differential Equations in Physiological Control Systems"],"prefix":"10.1155","volume":"2012","author":[{"given":"Qi","family":"Wang","sequence":"first","affiliation":[]},{"given":"Jiechang","family":"Wen","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2012,12,25]]},"reference":[{"key":"e_1_2_7_1_2","doi-asserted-by":"publisher","DOI":"10.1126\/science.267326"},{"key":"e_1_2_7_2_2","first-page":"156","article-title":"Dynamical diseases and bifurcations: understanding functional disorders in physiological systems, Funkt","volume":"1","author":"Mackey M. 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