© 2015 World Scientific Publishing Company. We give the normal forms of all polynomial differential systems in R3 which have a nondegenerate or degenerate quadric as an invariant algebraic surface. We also characterize among these systems those which have a Darboux invariant constructed uniquely using the invariant quadric, giving explicitly their expressions. As an example, we apply the obtained results in the determination of the Darboux invariants for the Chen system with an invariant quadric.
|Journal||International Journal of Bifurcation and Chaos in Applied Sciences and Engineering|
|Publication status||Published - 25 Jan 2015|
- Darboux integrability
- Darboux invariant
- Polynomial differential systems
- invariant quadric