Geodesic
On integrals, Hamiltonian and metriplectic formulations of polynomial systems in 3D
Theoretical and applied mechanics, Tome 44 (2017) no. 1, p. 15

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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.
DOI : 10.2298/TAM161118001E
Classification : 37K10, 70G45
Keywords: Darboux integrability method, the reduced three-wave interaction problem, Rabinovich system, Hindmarsh--Rose model, oregonator model, metriplectic Structure, Nambu-Poisson brackets 
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, p. 15 . doi: 10.2298/TAM161118001E
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     title = {On integrals, {Hamiltonian} and metriplectic formulations of polynomial systems in {3D}},
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