Multiple limit cycles for the continuous model of the rock–scissors–paper game between bacteriocin producing bacteria

•Two limit cycles for the continuous model of the rock–scissors–paper (RSP) game is constructed.•The Hopf bifurcation method is used for the construction of limit cycles.•The results give a partial answer to an open question posed by Neumann and Schuster.

In this paper we construct two limit cycles with a heteroclinic polycycle for the three-dimensional continuous model of the rock–scissors–paper (RSP) game between bacteriocin producing bacteria. Our construction gives a partial answer to an open question posed by Neumann and Schuster (2007) concerning how many limit cycles can coexist for the RSP game.