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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Periodic solutions of a periodic delay predator-prey system


Author: Li Yongkun
Journal: Proc. Amer. Math. Soc. 127 (1999), 1331-1335
MSC (1991): Primary 34K15, 34K20, 92A15
Published electronically: January 28, 1999
MathSciNet review: 1646198
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Abstract | References | Similar Articles | Additional Information

Abstract: The existence of a positive periodic solution for

\begin{equation*}\begin{cases} \frac{\mathrm{d}H(t)}{\mathrm{d}t}=r(t)H(t) \left[1-\frac{H(t-\tau(t))}{K(t)}\right] -\alpha(t)H(t) P(t),\\ \frac{\mathrm{d}P(t)}{\mathrm{d}t}=-b(t)P(t)+\beta(t)P(t)H(t-\sigma(t)) \end{cases} \end{equation*}

is established, where $r$, $K$, $\alpha$, $b$, $\beta$ are positive periodic continuous functions with period $\omega>0$, and $\tau$, $\sigma$ are periodic continuous functions with period $\omega$.


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Additional Information

Li Yongkun
Affiliation: Department of Mathematics, Yunnan University, Kunming, Yunnan 650091, People’s Republic of China
Email: yklie@ynu.edu.cn

DOI: http://dx.doi.org/10.1090/S0002-9939-99-05210-7
PII: S 0002-9939(99)05210-7
Keywords: Delay equation, predator-prey system, periodic solution
Received by editor(s): March 5, 1997
Published electronically: January 28, 1999
Additional Notes: The author was partially supported by the ABF of Yunnan Province of China
Communicated by: Suncica Canic
Article copyright: © Copyright 1999 American Mathematical Society