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Periodic solutions of a periodic delay predator-prey system

Author(s): Li Yongkun
Journal: Proc. Amer. Math. Soc. 127 (1999), 1331-1335.
MSC (1991): Primary 34K15, 34K20, 92A15
Posted: January 28, 1999
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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 , , $\alpha$ , , $\beta$ are positive periodic continuous functions with period $\omega>0$ , and $\tau$ , $\sigma$ are periodic continuous functions with period $\omega$ .

References:

1.: H. I. Freedman and J. Wu, Periodic solutions of single-species models with periodic delay, SIAM J. Math. Anal. 23 (1992), 689-701. MR 93e:92012
2.: Y. Kuang, Delay Differential Equations with Applications in Population Dynamics, Academic Press, New York, 1993. MR 94f:34001
3.: R. M. May, Stability and Complexity in Model Ecosystems, Princeton Univ. Press, Princeton, NJ, 1974.
4.: R. E. Gaines and J. L. Mawhin, Coincidence Degree and and Non-linear Differential Equations, Springer, Berlin, 1977. MR 58:30551

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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: 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
Posted: January 28, 1999
Additional Notes: The author was partially supported by the ABF of Yunnan Province of China
Communicated by: Suncica Canic
Copyright of article: Copyright 1999, American Mathematical Society


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