Predator-prey systems with a perturbed periodic carrying capacity (Q1095070)

The predator-prey model \[ x'=xg(x,K(t))-y^ mp(x),\quad y'=y[- s+cy^{m-1}p(x)-q(y)] \] is considered, where x is the number of prey, y is the number of predators, g is the specific growth rate of the prey in the absence of predators, p(x) is the predator response, c is the biomass conversion constant; \(K_ 0\) is the constant carrying capacity of the environment and \(K(t)=K_ 0+\epsilon k(t)\), \(k(t+\omega)=k(t)\), \(s+q(y)\) is the predator-specific death rate; \(0\leq m<1\) is the mutual interference constant. Non-critical cases and critical cases are investigated for existence and stability of periodic solutions.