<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">GUANGYING LV</style></author><author><style face="normal" font="default" size="100%">JINQIAO DUAN</style></author><author><style face="normal" font="default" size="100%">LIANG WANG</style></author><author><style face="normal" font="default" size="100%">JIANG-LUN WU</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">IMPACTS OF NOISE ON ORDINARY DIFFERENTIAL EQUATIONS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">35K20</style></keyword><keyword><style  face="normal" font="default" size="100%">60H15</style></keyword><keyword><style  face="normal" font="default" size="100%">60H40</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2018</style></year><pub-dates><date><style  face="normal" font="default" size="100%">03/2018</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/27/2/2.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">27</style></volume><pages><style face="normal" font="default" size="100%">12</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper, we consider the impacts of noise on ordinary differential&amp;nbsp;equations. We first prove that the weak noise can change the value of equilibrium&amp;nbsp;and the strong noise can destroy the stability of equilibrium. Then we consider the&amp;nbsp;competition between the nonlinear term and noise term, which shows that noise can&amp;nbsp;induce singularities (finite time blow up of solutions) and that the nonlinear term&amp;nbsp;can prevent the singularities. Besides that, some simulations are given in order to&amp;nbsp;illustrate our results.&lt;/p&gt;
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