<?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%">SNEZHANA HRISTOVA</style></author><author><style face="normal" font="default" size="100%">PETER KOPANOV</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">STABILITY OF NEURAL NETWORKS WITH RANDOM IMPULSES</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%">34A37</style></keyword><keyword><style  face="normal" font="default" size="100%">34D20</style></keyword><keyword><style  face="normal" font="default" size="100%">34F99</style></keyword><keyword><style  face="normal" font="default" size="100%">92B20</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%">10/2018</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/27/4/7.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 class=&quot;rtejustify&quot;&gt;One of the main properties of solutions of neural networks is stability&amp;nbsp;and often the direct Lyapunov method is used to study stability properties. We consider the Hopfield’s graded response neural network in the case when the neurons are&amp;nbsp;subject to a certain impulsive state displacement at random exponentially distributed&amp;nbsp;moments. It changes significantly the behavior of the solutions because they are not&amp;nbsp;deterministic ones but they are stochastic processes. We examine the stability of the&amp;nbsp;equilibrium of the model. Some sufficient conditions for p-moment stability of equilibrium of neural networks with time varying self-regulating parameters of all units&amp;nbsp;and time varying functions of the connection between two neurons in the network are&amp;nbsp;obtained. These sufficient conditions are explicitly expressed in terms of the parameters of the system and hence they are easily verifiable. We illustrate our theory on&amp;nbsp;a particular nonlinear neural network.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">4</style></issue><section><style face="normal" font="default" size="100%">791</style></section></record><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%">RAVI AGARWAL</style></author><author><style face="normal" font="default" size="100%">DONAL O’REGAN</style></author><author><style face="normal" font="default" size="100%">SNEZHANA HRISTOVA</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">MONOTONE-ITERATIVE TECHNIQUES FOR MILD SOLUTIONS OF THE INITIAL VALUE PROBLEM FOR CAPUTO FRACTIONAL DIFFERENTIAL EQUATIONS WITH NON-INSTANTANEOUS IMPULSES</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%">34A37</style></keyword><keyword><style  face="normal" font="default" size="100%">34E08</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2017</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2017</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/26/2/2.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">26</style></volume><pages><style face="normal" font="default" size="100%">26</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;The main aim of the paper is to suggest some algorithms to approximately solve the initial value problem for scalar nonlinear Caputo fractional differential equations with noninstantaneous impulses. The impulses start abruptly at some points and their action continue on given finite intervals. We study the case when the right hand side of the equations are monotonic functions. Several types of mild lower and mild upper solutions to the problem are defined and used in the algorithms. The convergence of the successive approximations is established. A generalization of the logistic equation is given to illustrate the results.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">2</style></issue><section><style face="normal" font="default" size="100%">211</style></section></record></records></xml>