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Zbl 1215.34104
Wang, Lin-Lin; Fan, Yong-Hong
Note on permanence and global stability in delayed ratio-dependent predator-prey models with monotonic functional responses.
(English)
[J] J. Comput. Appl. Math. 234, No. 2, 477-487 (2010). ISSN 0377-0427

This paper considers a general delayed ratio-dependent predator-prey model where all the coefficients are positive periodic and continuous functions. Sufficient conditions for the permanence and global stability are obtained when the functional response function $g$ is monotonic. Moreover, the permanence result improves Theorem 2.1 in [{\it Y.-H. Fan} and {\it W.-T. Li}, Nonlinear Anal., Real World Appl. 8, No.~2, 424--434 (2007; Zbl 1152.34368)] and the condition that guarantees the existence of positive periodic solutions generalizes the corresponding result by {\it M. Fan, Q. Wang} and {\it X. Zou} [Proc. R. Soc. Edinb., Sect. A, Math. 133, No.~1, 97--118 (2003; Zbl 1032.34044)] and {\it W. T. Li} and {\it L. Wang} [J. Comput. Appl. Math. 180, No.~2, 293--309 (2005; Zbl 1069.34100)].
[Shengqiang Liu (Harbin)]
MSC 2000:
*34K60 Applications of functional-differential equations
92D25 Population dynamics
34K20 Stability theory of functional-differential equations
34K25 Asymptotic theory of functional-differential equations

Keywords: predator-prey model; ratio dependent; monotonic response function; permanence; global stability

Citations: Zbl 1152.34368; Zbl 1069.34100; Zbl 1032.34044

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