| Title:
|
Positive periodic solution for ratio-dependent $n$-species discrete time system (English) |
| Author:
|
Tang, Mei-Lan |
| Author:
|
Liu, Xin-Ge |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
56 |
| Issue:
|
6 |
| Year:
|
2011 |
| Pages:
|
577-589 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper, sharp a priori estimate of the periodic solutions is obtained for the discrete analogue of the continuous time ratio-dependent predator-prey system, which is governed by nonautonomous difference equations, modelling the dynamics of the $n-1$ competing preys and one predator having nonoverlapping generations. Based on more precise a priori estimate and the continuation theorem of the coincidence degree, an easily verifiable sufficient criterion of the existence of positive periodic solutions is established. The result obtained in this paper greatly improves the existing results. (English) |
| Keyword:
|
ratio-dependent |
| Keyword:
|
predator-prey system |
| Keyword:
|
periodic solution |
| Keyword:
|
a priori estimate |
| MSC:
|
34C25 |
| MSC:
|
39A12 |
| MSC:
|
39A22 |
| MSC:
|
39A23 |
| MSC:
|
92D25 |
| idZBL:
|
Zbl 1249.39008 |
| idMR:
|
MR2886239 |
| DOI:
|
10.1007/s10492-011-0034-z |
| . |
| Date available:
|
2011-12-16T15:07:52Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141768 |
| . |
| Reference:
|
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| Reference:
|
[2] Ding, X., Lu, C., Liu, M. Z.: Periodic solutions for a semi-ratio-dependent predator-prey system with nonmonotonic functional response and time delay.Nonliear Anal., Real World Appl. 9 (2008), 762-775. Zbl 1152.34046, MR 2392373 |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
[8] Gaines, R. E., Mawhin, J. L.: Coincidence Degree, and Nonlinear Differential Equations.Lect. Notes Math., Vol. 568 Springer Berlin (1977). Zbl 0339.47031, MR 0637067, 10.1007/BFb0089537 |
| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| . |
