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In [1], we have presented the theoretical background for finding theElementary Invariants for a 3D system of first order rational differentialequations (1ODEs). We have also provided an algorithm to find such Invariants.Here we introduce new theoretical results that will lead to a novel, moreefficient, approach to determine these invariants. Furthermore, one importantaspect of such dynamical systems is that the integrability can be an issue. Wewill show that the present theoretical development allows for an Integrabilityanalysis in the case where the system has free parameters.

The search for Invariants for 3D Systems of 1ODEs - a new Method and Integrability Analysis