{"title":"具有时滞的四维神经网络模型的动力学行为","authors":"Changjin Xu, Peiluan Li","doi":"10.1155/2012/397146","DOIUrl":null,"url":null,"abstract":"A four-dimensional neural network model with delay is investigated. With the help of the theory of delay differential equation and Hopf bifurcation, the conditions of the equilibrium undergoing Hopf bifurcation are worked out by choosing the delay as parameter. Applying the normal form theory and the center manifold argument, we derive the explicit formulae for determining the properties of the bifurcating periodic solutions. Numerical simulations are performed to illustrate the analytical results.","PeriodicalId":7288,"journal":{"name":"Adv. Artif. Neural Syst.","volume":"29 1","pages":"397146:1-397146:11"},"PeriodicalIF":0.0000,"publicationDate":"2012-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Dynamical Behavior in a Four-Dimensional Neural Network Model with Delay\",\"authors\":\"Changjin Xu, Peiluan Li\",\"doi\":\"10.1155/2012/397146\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A four-dimensional neural network model with delay is investigated. With the help of the theory of delay differential equation and Hopf bifurcation, the conditions of the equilibrium undergoing Hopf bifurcation are worked out by choosing the delay as parameter. Applying the normal form theory and the center manifold argument, we derive the explicit formulae for determining the properties of the bifurcating periodic solutions. Numerical simulations are performed to illustrate the analytical results.\",\"PeriodicalId\":7288,\"journal\":{\"name\":\"Adv. Artif. Neural Syst.\",\"volume\":\"29 1\",\"pages\":\"397146:1-397146:11\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2012-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Adv. Artif. Neural Syst.\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1155/2012/397146\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Adv. Artif. Neural Syst.","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1155/2012/397146","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Dynamical Behavior in a Four-Dimensional Neural Network Model with Delay
A four-dimensional neural network model with delay is investigated. With the help of the theory of delay differential equation and Hopf bifurcation, the conditions of the equilibrium undergoing Hopf bifurcation are worked out by choosing the delay as parameter. Applying the normal form theory and the center manifold argument, we derive the explicit formulae for determining the properties of the bifurcating periodic solutions. Numerical simulations are performed to illustrate the analytical results.