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.


34D05 Asymptotic properties of solutions to ordinary differential equations
92D25 Population dynamics (general)
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