Based on sexual reproduction and birth matrix-mating rule model (BMMR model), the following representatives of birth and death rates of sexual population were obtained: (dN/dt) b=N 2g b(N)=bN 2(1-uN+w 1N 2),(dN/dt) d=Ng d(N)=dN(1+vN+w 2N 2). Tus predator-prey system can present limit cycles with cusp geometry. The sexual population has humped curves of natural increase rate of individuals as function of population size and two equilibrium points: stable S and unstable X, S>X, an asexual population can only have one equilibrium point, i.e. stable S.
