[1]刘华祥,曾广洪.一类具季节性时变参数和周期时滞的浮游植物-浮游动物模型的正周期解[J].江西师范大学学报(自然科学版),2012,(05):506-511.
 LIU Hua-xiang,ZENG Guang-hong.The Existence of Positive Periodic Solutions for a Phytoplankton-Zooplankton Model with Seasonally Varying Parameters and Time Delays[J].,2012,(05):506-511.
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一类具季节性时变参数和周期时滞的浮游植物-浮游动物模型的正周期解()
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《江西师范大学学报》(自然科学版)[ISSN:1006-6977/CN:61-1281/TN]

卷:
期数:
2012年05期
页码:
506-511
栏目:
出版日期:
2012-10-01

文章信息/Info

Title:
The Existence of Positive Periodic Solutions for a Phytoplankton-Zooplankton Model with Seasonally Varying Parameters and Time Delays
作者:
刘华祥;曾广洪
广东海洋大学理学院数学系, 广东 湛江 524088;江西师范大学数学与信息科学学院, 江西 南昌330022
Author(s):
LIU Hua-xiang ZENG Guang-hong
关键词:
浮游植物-浮游动物时滞正周期解叠合度的延拓定理拓扑度
Keywords:
phytoplankton-zooplankton time delay positive periodic solution the continuation theorem of coincidence degree topological degree
分类号:
O29
文献标志码:
A
摘要:
提出了一类具季节性时变参数和周期时滞的有3种浮游生物种群组成的动力学模型,包括无毒浮游植物(NTP)、有毒浮游植物(TPP)和浮游动物(Z),并研究了该系统的正周期解的存在性.通过运用叠合度理论中的延拓定理,建立了保证该系统至少存在1个正周期解的充分条件,所得结果适用于相应的无时滞和离散时滞系统.
Abstract:
A three-dimensional ratio-dependent phytoplankton- zooplankton model with time delay and seasonal effects consisting of non-toxic phytoplankton(NTP), toxin producing phytoplankton (TPP) and zooplankton (Z) is considered. The existence of positive periodic solutions for the systems is studied. By using the continuation theorem of coincidence degree theory, a set of sufficient conditions are obtained for the existence of at least one strictly positive periodic solution. The results are established for the underlying systems without time delay or with discrete time delay.

参考文献/References:

[1] Maynard-Smith J. Models in ecology [M]. Cambridge: Cambridge University, 1974.
[2] Chattopadhyay J. Effect of toxic substances on a two-species competitive system [J]. Ecological Modelling, 1996, 84(1/2/3): 287-289.
[3] Mukhopadhyay A, Chattopadhyay J, Tapaswi P K. A delay differential equations model of plankton allelopathy [J]. Math Biosci, 1998, 149(2): 167-189.
[4] Tapaswi P K, Mukhopadhyay A. Effects of environmental fluctuation on plankton allelopathy [J]. J Math Biol, 1999, 39(1): 39-58.
[5] 宋新宇, 陈兰荪. 一类浮游生物植化相克时滞微分方程的周期解 [J]. 数学物理学报, 2003, 23A (1): 8- 13.
[6] Chattopadhyay J, Sarkar R R, Pal S. Mathematical modelling of harmful algal blooms supported by experimental findings [J]. Ecol Comp, 2004, 1(3): 225–235.
[7] Pal S, Samrat Chatterjee, Krishna Pada Das, et al. Role of competition in phytoplankton population for the occurrence and control of plankton bloom in the presence of environmental fluctuations [J]. Ecological Modeling, 2009, 220(2): 96-110.
[8] Arditi R, Ginzburg L R. Coupling in predator-prey dynamics: Ration-dependence [J]. J Theor Biol, 1989, 139(3): 311-326.
[9] Gaines R E, Mawhin J L. Coincidence degree and nonlinear differential equations [M]. Berlin, New York: Springer, 1977.
[10] 向昭红. 一类食物链条系统的正周期解 [J]. 江西师范大学学报: 自然科学版, 2001, 25(4): 342-347.

更新日期/Last Update: 1900-01-01