Geodesic
On integrals, Hamiltonian and metriplectic formulations of polynomial systems in 3D
Theoretical and applied mechanics, Tome 44 (2017) no. 1

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

The first integrals of the reduced three-wave interaction problem, the Rabinovich system, the Hindmarsh--Rose model, and the Oregonator model are derived using the method of Darboux polynomials. It is shown that, the reduced three-wave interaction problem, the Rabinovich system, the Hindmarsh--Rose model can be written in a bi-Hamiltonian/Nambu metriplectic form.
Keywords: Darboux integrability method, the reduced three-wave interaction problem, Rabinovich system, Hindmarsh--Rose model, oregonator model, metriplectic Structure, Nambu-Poisson brackets 
@article{TAM_2017_44_1_a3,
     author = {O\u{g}ul Esen and Anindya Ghose Choudhury and Partha Guha},
     title = {On integrals, {Hamiltonian} and metriplectic formulations of polynomial systems in {3D}},
     journal = {Theoretical and applied mechanics},
     pages = {15 - 34},
     publisher = {mathdoc},
     volume = {44},
     number = {1},
     year = {2017},
     url = {http://geodesic.mathdoc.fr/item/TAM_2017_44_1_a3/}
}
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Oğul Esen; Anindya Ghose Choudhury; Partha Guha. On integrals, Hamiltonian and metriplectic formulations of polynomial systems in 3D. Theoretical and applied mechanics, Tome 44 (2017) no. 1. http://geodesic.mathdoc.fr/item/TAM_2017_44_1_a3/