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Zbl 1111.34039
Chen, Fengde
Permanence of periodic Holling type predator--prey system with stage structure for prey. (English)
[J] Appl. Math. Comput. 182, No. 2, 1849-1860 (2006). ISSN 0096-3003

Summary: We study the permanence of the following periodic Holling-type predator-prey system with stage structure for prey $$\align \dot x_1(t) & =a(t)x_2(t)-b(t)x_1(t) -d(t)x^2_1(t)-\frac{e(t)x^\gamma_1(t)} {p(t)+ x^\gamma_1(t)}y(t),\\ \dot x_2(t)& =c(t)x_1(t)-f(t)x^2_2(t),\\ \dot y(t) &=y(t)\left(-g(t)+\frac{h(t)x_1^\gamma(t)} {p(t)+x^\gamma_1(t)}-q(t)y(t)\right).\endalign$$ A sufficient and necessary condition which guarantees the predator and the prey species to be permanent is obtained. Some new results are obtained.

MSC 2000:: *34D05 Asymptotic stability of ODE
34C60 Applications of qualitative theory of ODE
92D25 Population dynamics

Keywords: nonautonomous; Holling type; predator--prey; permanence; stage structure

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