Necessary and sufficient conditions for the existence of periodic orbits in a Lotka-Volterra system. (Q1406531)

The interesting paper deals with three species Lotka-Volterra systems of the form \[ x_i'=x_i(b-\sum_{j=1}^3a_{ij}x_j),\quad i=1,2,3.\tag{1} \] The author derives necessary and sufficient conditions for the existence of periodic orbits to (1), by extending the Darboux method to the third dimension. This study also covers some stability analysis for periodic orbits and Hopf bifurcations.