On Integrals, Hamiltonian and Metriplectic Formulations of 3D Polynomial Systems

2016/08/04 by Oğul Esen, Anindya Ghose Choudhury, Partha Guha · 1 citation
Mathematics · Physics and Astronomy · #math-ph #math.MP #math.SG #msc:37K10 #msc:70G45

paper · pdf · doi:10.2298/tam161118001e

arxiv created 2016/08/04 · arxiv updated 2017/08/02

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.

Cited by

• Structure preserving integration of 3D dissipative bi-Hamiltonian/Nambu systems

Related

• Existence of Hamiltonian Structure in 3D
• Darboux polynomial matrices: the classical Massive Thirring Model as study case
• Homogeneous Darboux polynomials and generalising integrable ODE systems
• Relations between different Hamiltonian forms of the third Painlevé equation
• On novel Hamiltonian descriptions of some three-dimensional non-conservative systems