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 
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     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},
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}
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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/