{"title":"GRN和ANN网络中的周期吸引子","authors":"Ogorelova Diana, Sadyrbaev Felix","doi":"10.1109/ELECS55825.2022.00036","DOIUrl":null,"url":null,"abstract":"We provide the conditions for the existence of a periodic solution in two-dimensional systems of ordinary differential equations, which arise in the theory of genetic and artificial neural networks. The proof is based on Poincare-Andronov-Hopf bifurcation. Multidimensional attractors can be constructed using the two-dimensional ones. Illustrations and examples are provided.","PeriodicalId":320259,"journal":{"name":"2022 6th European Conference on Electrical Engineering & Computer Science (ELECS)","volume":"9 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Periodic attractors in GRN and ANN networks\",\"authors\":\"Ogorelova Diana, Sadyrbaev Felix\",\"doi\":\"10.1109/ELECS55825.2022.00036\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We provide the conditions for the existence of a periodic solution in two-dimensional systems of ordinary differential equations, which arise in the theory of genetic and artificial neural networks. The proof is based on Poincare-Andronov-Hopf bifurcation. Multidimensional attractors can be constructed using the two-dimensional ones. Illustrations and examples are provided.\",\"PeriodicalId\":320259,\"journal\":{\"name\":\"2022 6th European Conference on Electrical Engineering & Computer Science (ELECS)\",\"volume\":\"9 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-12-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2022 6th European Conference on Electrical Engineering & Computer Science (ELECS)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/ELECS55825.2022.00036\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2022 6th European Conference on Electrical Engineering & Computer Science (ELECS)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ELECS55825.2022.00036","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We provide the conditions for the existence of a periodic solution in two-dimensional systems of ordinary differential equations, which arise in the theory of genetic and artificial neural networks. The proof is based on Poincare-Andronov-Hopf bifurcation. Multidimensional attractors can be constructed using the two-dimensional ones. Illustrations and examples are provided.