Language:   Search:   Contact
Zentralblatt MATH has released its new interface!
For an improved author identification, see the new author database of ZBMATH.

Query:
Fill in the form and click »Search«...
Format:
Display: entries per page entries
Zbl 1152.34368
Fan, Yong-Hong; Li, Wan-Tong
Permanence in delayed ratio-dependent predator-prey models with monotonic functional responses.
(English)
[J] Nonlinear Anal., Real World Appl. 8, No. 2, 424-434 (2007). ISSN 1468-1218

Summary: In this paper, sufficient conditions for permanence of the general delayed ratio-dependent predator-prey model $$\cases x^{\prime}(t)=x(t)[a(t)-b(t)x(t)]-c(t)g\left(\frac{x(t)}{y(t)}\right)y(t),\\ y^{\prime}(t)=y(t)\left[e(t)g\left(\frac{x(t-\tau)}{y(t-\tau)}\right)-d(t)\right],\endcases$$ \newline are obtained when functional response $g$ is monotonic, where $a(t), b(t), c(t), d(t)$ and $e(t)$ are all positive periodic continuous functions with period $\omega >0, \tau$ is a positive constant. We find that the conditions on existence of a positive periodic solution imply the permanence of the above system. As applications, some examples are given.
MSC 2000:
*34K13 Periodic solutions of functional differential equations
92D25 Population dynamics
34C25 Periodic solutions of ODE

Keywords: predator-prey model; ratio-dependent; monotonic response functional; permanence

Cited in: Zbl 1215.34104

Highlights
Master Server