Permanence and stability of a stage-structured predator-prey model. (English) Zbl 0997.34069

This is a well written and timely paper that provides a nice qualitative analysis of a delayed Holling-type II ratio-dependent predator-prey model. The time delay (maturation time) is carefully introduced and it is shown that for small delay, the system is globally stable, if a positive steady state exists. The method makes use of fluctuation lemma and Lyapunov functional arguments. However, the local stability section may not completely true since it uses a standard theorem that guaranteed to work only for systems with delay independent parameters. To be rigorous, the authors need to use the recently established results by E. Beretta and Y. Kuang [SIAM J. Math. Anal. 33, No. 5, 1144-1165 (2002; Zbl 1013.92034)].
Reviewer: Yang Kuang (Tempe)


34K20 Stability theory of functional-differential equations
92D25 Population dynamics (general)


Zbl 1013.92034
Full Text: DOI


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