Research on stability and Hopf bifurcation of marine ecosystem dynamics models

SHI Honghua; HU Long; FANG Guohong; WEI Zexun; SHEN Chengcheng; LIU Yongzhi

doi:10.1007/s13131-016-0809-x

Article Contents

Article Navigation > Acta Oceanologica Sinica > 2016 > 35(4): 124-132

SHI Honghua, HU Long, FANG Guohong, WEI Zexun, SHEN Chengcheng, LIU Yongzhi. Research on stability and Hopf bifurcation of marine ecosystem dynamics models[J]. Acta Oceanologica Sinica, 2016, 35(4): 124-132. doi: 10.1007/s13131-016-0809-x

Citation:

SHI Honghua, HU Long, FANG Guohong, WEI Zexun, SHEN Chengcheng, LIU Yongzhi. Research on stability and Hopf bifurcation of marine ecosystem dynamics models[J]. Acta Oceanologica Sinica, 2016, 35(4): 124-132. doi: 10.1007/s13131-016-0809-x

Citation:

PDF( 4901 KB)

Research on stability and Hopf bifurcation of marine ecosystem dynamics models

doi: 10.1007/s13131-016-0809-x

1.
First Institute of Oceanography, State Oceanic Administration, Qingdao 266061, China
2.
School of Mathematics, Shandong University, Jinan 250100, China
3.
First Institute of Oceanography, State Oceanic Administration, Qingdao 266061, China;College of Environmental Science and Engineering, Ocean University of China, Qingdao 266100, China
4.
Key Laboratory of Physical Oceanography, Ocean University of China, Qingdao 266003, China

Received Date: 2015-07-20
Rev Recd Date: 2015-09-21

Abstract

Abstract

The predictability of marine ecosystem dynamics models is one of the most vital factors to limit their practical applications, of which the stability is the fundamental condition. In order to discuss the stability and Hopf bifurcation of marine ecosystem dynamics models, an approach based on a theorem termed dimension reduction was proposed and further applied in the mass-conservative nutrient-phytoplankton-zooplankton-detritus(NPZD) model in this paper. Results showed that the nonsingular equilibrium point of NPZD model was analytically stable in use of the dimension reduction theorem and the Hopf bifurcation might occur when model parameters changed along the threshold values. The analytical results of the NPZD model were further verified by numerical simulation in this study. It can be concluded that this approach based on the dimension reduction theorem is well applicable to the theoretical analysis of a kind of stability problems and Hopf bifurcation of mass-conservative systems.
- marine ecosystem,
- mass-conservative,
- NPZD,
- stability,
- Hopf bifurcation

FullText(HTML)

References(41)

References

Bricker S B, Ferreira J G, Simas T. 2003. An integrated methodology for assessment of estuarine trophic status. Ecological Model-ling, 169(1):39-60

Chen Changsheng. 2003. Marine Ecosystem Dynamics and Modeling(in Chinese). Beijing:Higher Education Press

Chen Changsheng, Ji Rubao, Zheng Lianyuan, et al. 1999. Influences of physical processes on the ecosystem in Jiaozhou Bay:A coupled physical and biological model experiment. Journal of Geophysical Research, 104(C12):29925-29949

Cossarini G, Solidoro C. 2008. Global sensitivity analysis of a tropho-dynamic model of the Gulf of Trieste. Ecological Modelling, 212(1-2):16-27

Costanza R, D'Agre R, de Groot R, et al. 1997. The value of the world's ecosystem services and natural capital. Nature, 387(6630):253-260

Edwards A M, Bees M A. 2001. Generic dynamics of a simple plank-ton population model with a non-integer exponent of closure. Chaos, Solitons and Fractals, 12(2):289-300

Edwards A M, Brindley J. 1996. Oscillatory behaviour in a three-com-ponent plankton population model. Dynamics and Stability of Systems, 11(4):347-370

Edwards A M, Brindley J. 1999. Zooplankton mortality and the dy-namical behaviour of plankton population models. Bulletin of Mathematical Biology, 61(2):303-339

Edwards A M, Yool A. 2000. The role of higher predation in plankton population models. Journal of Plankton Research, 22(6):1085-1112

Fasham M J R, Ducklow H W, McKelvie S M. 1990. A nitrogen-based model of plankton dynamics in the oceanic mixed layer. Journ-al of Marine Research, 48(3):591-639

Fei Zunle. 1984. An estimation of the diffuse attenuation coefficient in offshore waters. J Oceanogr Huang Hai & Bohai Seas(in Chinese), 2(1):26-29

Feng Shizuo, Zhang Jing, Wei Hao. 2007. An Introduction to Environ-mental Dynamics of the Bohai Sea(in Chinese). Beijing:Sci-ence Press

Franks P J S, Chen Changsheng. 1996. Plankton production in tidal fronts:A model of Georges Bank in summer. Journal of Marine Research, 54(4):631-651

Franks P J S, Wroblewski J S, Flierl G R. 1986. Behavior of a simple plankton model with food-level acclimation by herbivores. Marine Biology, 91(1):121-129

Fransz H G, Verhagen J H G. 1985. Modelling research on the produc-tion cycle of phytoplankton in the Southern Bight of the North Sea in relation to riverborne nutrient loads. Netherlands Journ-al of Sea Research, 19(3-4):241-250

Fujii M, Yoshie N, Yamanaka Y, et al. 2005. Simulated biogeochemic-al responses to iron enrichments in three high nutrient, low chlorophyll(HNLC) regions. Progress in Oceanography, 64(2-4):307-324

Gao Huiwang, Feng Shizuo, Guan Yuping. 1998. Modelling annual cycles of primary production in different regions of the Bohai Sea. Fisheries Oceanography, 7(3-4):258-264

Gao Meng, Shi Honghua, Li Zizhen. 2009. Chaos in a seasonally and periodically forced phytoplankton-zooplankton system. Non-linear Analysis:Real World Applications, 10(3):1643-1650

Granéli E, Weberg M, Salomon P S. 2008. Harmful algal blooms of al-lelopathic microalgal species:The role of eutrophication. Harmful Algae, 8(1):94-102

Hale J K, Ko.ak H. 1991. Dynamics and Bifurcations(Texts in Ap-plied Mathematics Volume 3). New York:Springer-Verlag

Halpern B S, Longo C, Hardy D, et al. 2012. An index to assess the health and benefits of the global ocean. Nature, 488(7413):615-620

Halpern B S, Walbridge S, Selkoe K A, et al. 2008. A global map of hu-man impact on marine ecosystems. Science, 319(5865):948-952

Heimsund B O, Berntsen J. 2004. On a class of ocean model instabilit-ies that may occur when applying small time steps, implicit methods, and low viscosities. Ocean Modelling, 7(1-2):135-144

Hirsch M W, Smale S, Devaney R L. 2004. Differential Equations, Dy-namical Systems and an Introduction to Chaos. 2nd ed. Ams-terdam:Elsevier/Academic Press

Holling C S. 1973. Resilience and stability of ecological systems. An-nual Review of Ecology and Systematics, 4(1):1-23

Jackson J B C, Kirby M X, Berger W H, et al. 2001. Historical overfish-ing and the recent collapse of coastal ecosystems. Science, 293(5530):629-638

Kirk P D W, Toni T, Stumpf M P H. 2008. Parameter inference for bio-chemical systems that undergo a Hopf bifurcation. Biophysical Journal, 95(2):540-549

Kuznetsov Y A. 2004. Elements of Applied Bifurcation Theory. New York:Springer-Verlag

Liu Zhe, Wei Hao, Bai Jie, et al. 2007. Nutrients seasonal variation and budget in Jiaozhou Bay, China:A 3-dimensional physical-bio-logical coupled model study. Water, Air & Soil Pollution:Focus, 7(6):607-623

Lotze H K, Lenihan H S, Bourque B J, et al. 2006. Depletion, degrada-tion, and recovery potential of estuaries and coastal seas. Sci-ence, 312(5781):1806-1809

McCann K, Hastings A. 1997. Re-evaluating the omnivory-stability re-lationship in food webs. Royal Socociety of London Proceeding, 264(1385):1249-1254

McCreary J P, Kohler K E, Hood R R, et al. 1996. A four-component ecosystem model of biological activity in the Arabian Sea. Pro-gress in Oceanography, 37(3-4):193-240

Millennium Ecosystem Assessment(MA). 2005. Ecosystems and Hu-man Well-Being:Synthesis Report. Washington DC:Island Press

Morris D J, Speirs D C, Cameron A I, et al. 2014. Global sensitivity analysis of an end-to-end marine ecosystem model of the North Sea:Factors affecting the biomass of fish and benthos. Ecological Modelling, 273:251-263

Myers R A, Worm B. 2003. Rapid worldwide depletion of predatory fish communities. Nature, 423(6937):280-283

Steele J H. 1962. Environmental control of photosynthesis in the sea. Limnology & Oceanography, 7(2):137-150

Steele J H, Henderson E W. 1992. The role of predation in plankton models. Journal of Plankton Research, 14(1):157-172

Tian Rucheng, Chen Changsheng, Qi Jianhua, et al. 2015. Model study of nutrient and phytoplankton dynamics in the Gulf of Maine:Patterns and drivers for seasonal and interannual vari-ability. ICES Journal of Marine Science, 72(2):388-402

Vichi M, Masina S, Navarra A. 2007. A generalized model of pelagic biogeochemistry for the global ocean ecosystem. Part Ⅱ:Nu-merical simulations. Journal of Marine Systems, 64(1-4):110-134

Wang Hongli, Feng Jianfeng. 2006. Ecosystem Dynamics and Fore-casting of Algal Blooms(in Chinese). Tianjin:Tianjin Uni-versity Press

Zheng Wei, Shi Honghua, Fang Guohong, et al. 2012. Global sensitiv-ity analysis of a marine ecosystem dynamic model of the Sanggou Bay. Ecological Modelling, 247(4):83-94

Relative Articles

Supplements(0)

Cited By

Proportional views