Two limit cycles in three-dimensional Lotka-Volterra systems

Among the six classes of Zeemanʹs classification for three-dimensional Lotka-Volterra competitive systems with limit cycles, besides the heteroclinic cycle case (Case 27), we construct in three cases without heteroclinic cycle (Cases 26, 28, 29) two limit cycles. Our construction gives a partial answer to Hofbauer and Soʹs problem to these systems.