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.