On Integrals, Hamiltonian and Metriplectic Formulations of 3D Polynomial Systems
arXiv:1608.01507 · doi:10.2298/TAM161118001E
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.