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 \[ \begin{aligned} \dot x_1(t) & =a(t)x_2(t)-b(t)x_1(t) -d(t)x^2_1(t)-\frac{e(t)x^\gamma_1(t)} {p(t)+ x^\gamma_1(t)}y(t),\\ \dot x_2(t)& =c(t)x_1(t)-f(t)x^2_2(t),\\ \dot y(t) &=y(t)\left(-g(t)+\frac{h(t)x_1^\gamma(t)} {p(t)+x^\gamma_1(t)}-q(t)y(t)\right).\end{aligned} \] A sufficient and necessary condition which guarantees the predator and the prey species to be permanent is obtained. Some new results are obtained.


34D05 Asymptotic properties of solutions to ordinary differential equations
34C60 Qualitative investigation and simulation of ordinary differential equation models
92D25 Population dynamics (general)
Full Text: DOI


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