Mathematical analysis on deterministic and stochastic lake ecosystem models.
作者： Zhiwei Huang , , Gang Huang
DOI: 10.3934/MBE.2019237
关键词: Invariance principle 、 Stochastic modelling 、 Mathematics 、 Lyapunov function 、 Statistical physics 、 Ergodic theory 、 Stationary distribution 、 Plankton 、 Population model 、 Lake ecosystem
摘要: In this paper, we propose and study the deterministic stochastic lake ecosystem models to investigate impact of terrestrial organic matter upon persistence plankton populations. By constructing Lyapunov function using LaSalle's Invariance Principle, establish global properties model. The dynamical behavior solutions fits well with some experimental results. It is concluded that plays an important role in influencing interactions between phytoplankton zooplankton. Based on fluctuations ecosystem, further develop a stochastically perturbed Theoretic analysis implies model exists stationary distribution which ergodic. key point our enhance knowledge factors governing dynamics population models.
sci-hub.st 参考文章(29)
Sophia R.-J. Jang, Edward J. Allen, Deterministic and stochastic nutrient-phytoplankton- zooplankton models with periodic toxin producing phytoplankton Applied Mathematics and Computation. ,vol. 271, pp. 52- 67 ,(2015) , 10.1016/J.AMC.2015.08.065
Linning Qian, Qishao Lu, Qingguo Meng, Zhaosheng Feng, Dynamical behaviors of a prey–predator system with impulsive control Journal of Mathematical Analysis and Applications. ,vol. 363, pp. 345- 356 ,(2010) , 10.1016/J.JMAA.2009.08.048
Yongzhen Pei, Yunfei Lv, Changguo Li, Evolutionary consequences of harvesting for a two-zooplankton one-phytoplankton system Applied Mathematical Modelling. ,vol. 36, pp. 1752- 1765 ,(2012) , 10.1016/J.APM.2011.09.015
Chunyan Ji, Daqing Jiang, Ningzhong Shi, Analysis of a predator-prey model with modified Leslie-Gower and Holling-type II schemes with stochastic perturbation Journal of Mathematical Analysis and Applications. ,vol. 359, pp. 435- 440 ,(2009) , 10.1016/J.JMAA.2009.05.039
J. S. Wroblewski, Jorge L. Sarmiento, Glenn R. Flierl, An Ocean Basin Scale Model of plankton dynamics in the North Atlantic: 1. Solutions For the climatological oceanographic conditions in May Global Biogeochemical Cycles. ,vol. 2, pp. 199- 218 ,(1988) , 10.1029/GB002I003P00199
Michael T. Brett, Martin J. Kainz, Sami J. Taipale, Hari Seshan, Phytoplankton, not allochthonous carbon, sustains herbivorous zooplankton production Proceedings of the National Academy of Sciences of the United States of America. ,vol. 106, pp. 21197- 21201 ,(2009) , 10.1073/PNAS.0904129106
Anurani D. Persaud, Peter J. Dillon, Differences in zooplankton feeding rates and isotopic signatures from three temperate lakes Aquatic Sciences. ,vol. 73, pp. 261- 273 ,(2011) , 10.1007/S00027-010-0174-3
Amit Sharma, Anuj Kumar Sharma, Kulbhushan Agnihotri, Analysis of a toxin producing phytoplankton–zooplankton interaction with Holling IV type scheme and time delay Nonlinear Dynamics. ,vol. 81, pp. 13- 25 ,(2015) , 10.1007/S11071-015-1969-5
Urszula Foryś, Meihong Qiao, Anping Liu, Asymptotic dynamics of a deterministic and stochastic predator-prey model with disease in the prey species Mathematical Methods in the Applied Sciences. ,vol. 37, pp. 306- 320 ,(2014) , 10.1002/MMA.2783
J TRUSCOTT, J BRINDLEY, Ocean plankton populations as excitable media Bulletin of Mathematical Biology. ,vol. 56, pp. 981- 998 ,(1994) , 10.1016/S0092-8240(05)80300-3