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Permanence of periodic Holling type-IV predator-prey system with stage structure for prey. (English) Zbl 1156.34327
Summary: We study the permanence of the following periodic Holling type-IV predator-prey system with stage structure for prey
\begin{aligned} \dot x_1(t)=a(t) & x_2(t)-b(t)x_1(t)-d(t)x^2_1(t)-\frac{p(t)x_1(t)}{k(t)+x_1^2(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(t)}{k(t)+x_1^2(t)}-q(t)y(t)\right).\end{aligned}
Under certain assumptions, sufficient and necessary conditions which guarantee the predator and the prey species to be permanent are obtained.

##### MSC:
 34D05 Asymptotic properties of solutions to ordinary differential equations 92D25 Population dynamics (general)
##### Keywords:
nonautonomous; permanence; Holling type-IV; stage structure
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