Local integrability of a family of three-dimensional quadratic systems

We investigate the local integrability of a family of three dimensional quadratic systems in a neighborhood of ( 0 : − 1 : 1 ) resonant singular point. We find the necessary and sufficient conditions for the existence of two functionally independent first integrals of the system. Mechanisms for integrability for the systems are either time-reversibility or Darboux integrability.