{"title":"三维多项式系统的积分、哈密顿公式和三重公式","authors":"Ougul Esen, A. Choudhury, P. Guha","doi":"10.2298/TAM161118001E","DOIUrl":null,"url":null,"abstract":"We apply the Darboux integrability method to determine first integrals and Hamiltonian formulations of three dimensional polynomial systems; namely the reduced three-wave interaction problem, the Rabinovich system, the Hindmarsh-Rose model, and the oregonator model. Additionally, we investigate their Hamiltonian, Nambu-Poisson and metriplectic characters.","PeriodicalId":44059,"journal":{"name":"Theoretical and Applied Mechanics","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2016-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"On integrals, Hamiltonian and metriplectic formulations of polynomial systems in 3D\",\"authors\":\"Ougul Esen, A. Choudhury, P. Guha\",\"doi\":\"10.2298/TAM161118001E\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We apply the Darboux integrability method to determine first integrals and Hamiltonian formulations of three dimensional polynomial systems; namely the reduced three-wave interaction problem, the Rabinovich system, the Hindmarsh-Rose model, and the oregonator model. Additionally, we investigate their Hamiltonian, Nambu-Poisson and metriplectic characters.\",\"PeriodicalId\":44059,\"journal\":{\"name\":\"Theoretical and Applied Mechanics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2016-08-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Theoretical and Applied Mechanics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.2298/TAM161118001E\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MECHANICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Theoretical and Applied Mechanics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2298/TAM161118001E","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MECHANICS","Score":null,"Total":0}
On integrals, Hamiltonian and metriplectic formulations of polynomial systems in 3D
We apply the Darboux integrability method to determine first integrals and Hamiltonian formulations of three dimensional polynomial systems; namely the reduced three-wave interaction problem, the Rabinovich system, the Hindmarsh-Rose model, and the oregonator model. Additionally, we investigate their Hamiltonian, Nambu-Poisson and metriplectic characters.
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