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Homogeneous darboux polynomials and generalising integrable ODE systems
This is a pre-copy-editing, author-produced PDF of an article accepted for publication in [insert journal title] following peer review. The definitive publisher-authenticated version [insert complete citation information here] is available online at: http://www.aimsciences.org/article/doi/10.3934/jcd.2021001
We show that any system of ODEs can be modified whilst preserving its homogeneous Darboux polynomials. We employ the result to generalise a hierarchy of integrable Lotka-Volterra systems.