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Permanence of periodic Holling type predator–prey system with stage structure for prey. (English) Zbl 1111.34039

Summary: We study the permanence of the following periodic Holling-type predator-prey system with stage structure for prey

x ˙ 1 (t)=a(t)x 2 (t)-b(t)x 1 (t)-d(t)x 1 2 (t)-e(t)x 1 γ (t) p(t)+x 1 γ (t)y(t),x ˙ 2 (t)=c(t)x 1 (t)-f(t)x 2 2 (t),y ˙(t)=y(t)-g(t)+h(t)x 1 γ (t) p(t)+x 1 γ (t)-q(t)y(t)·

A sufficient and necessary condition which guarantees the predator and the prey species to be permanent is obtained. Some new results are obtained.

34D05Asymptotic stability of ODE
34C60Qualitative investigation and simulation of models (ODE)
92D25Population dynamics (general)