On integrals, Hamiltonian and metriplectic formulations of polynomial systems in 3D

Abstract

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