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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.

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