`a`
Mathematical Biosciences and Engineering (MBE)
 

Dynamical analysis of a toxin-producing phytoplankton-zooplankton model with refuge
Pages: 529 - 557, Issue 2, April 2017

doi:10.3934/mbe.2017032      Abstract        References        Full text (7548.0K)           Related Articles

Juan Li - Jiangsu Key Laborary for NSLSCS, Institute of Mathematics, School of Mathematics Science, Nanjing Normal University, Nanjing 210023, China (email)
Yongzhong Song - Jiangsu Key Laborary for NSLSCS, Institute of Mathematics, School of Mathematics Science, Nanjing Normal University, Nanjing 210023, China (email)
Hui Wan - Jiangsu Key Laborary for NSLSCS, Institute of Mathematics, School of Mathematics Science, Nanjing Normal University, Nanjing 210023, China (email)
Huaiping Zhu - Laboratory of Mathematical Parallel Systems (Lamps), Department of Mathematics and Statistics, York University, Toronto, ON, M3J 1P3, Canada (email)

1 H. Duan, R. Ma, X. Xu, F. Kong, S. Zhang, W. Kong, J. Hao and L. Shang, Two-decade reconstruction of algal blooms in China-Lake Taihu, Environ. Sci. Technol., 43 (2009), 3522-3528.
2 M. Wines, Spring Rain, Then Foul Algae in Ailing Lake Erie, Report of The New York Times, 2013. Available from: http://www.nytimes.com/2013/03/15/science/earth/algae-blooms-threaten-lake-erie.html?&_r=0.
3 W. McLean and J. Macdonald, CLAS: Colby Liberal Arts Symposium, Lake Erie Algal Blooms, 2014. Available from: http://digitalcommons.colby.edu/clas/2014/program/414/.
4 C. B. Lopez, E. B. Jewett, Q. Dortch, B. T. Walton and H. K. Hudnell, Scientific Assessment of Freshwater Harmful Algal Blooms, Interagency Working Group on Harmful Algal Blooms, Hypoxia, and Human Health of the Joint Subcommittee on Ocean Science and Technology. Washington, DC. 2008. Available from: https://www.whitehouse.gov/sites/default/files/microsites/ostp/frshh2o0708.pdf.
5 E. Beltrami and T. O. Carroll, Modeling the role of viral disease in recurrent phytoplankton blooms, J. Math. Biol., 32 (1994), 857-863.
6 J. Norberg and D. DeAngelis, Temperature effects on stocks and stability of a phytoplankton-zooplankton model and the dependence on light and nutrients, Ecol. Model., 95 (1997), 75-86.
7 B. Mukhopadhyay and R. Bhattacharyya, Modelling phytoplankton allelopathy in a nutrient-plankton model with spatial heterogeneity, Ecol. Model., 198 (2006), 163-173.
8 S. Pal, S. Chatterjee and J. Chattopadhyay, Role of toxin and nutrient for the occurrence and termination of plankton bloom results drawn from field observations and a mathematical model, Biosystems, 90 (2007), 87-100.
9 T. Saha and M. Bandyopadhyay, Dynamical analysis of toxin producing phytoplankton-zooplankton interactions, Nonlinear Anal-Real., 10 (2009), 314-332.       
10 Y. Lv, Y. Pei, S. Gao and C. Li, Harvesting of a phytoplankton-zooplankton model, Nonlinear Anal-Real., 11 (2010), 3608-3619.       
11 M. Bengfort, U. Feudel, F. M. Hilker and H. Malchow, Plankton blooms and patchiness generated by heterogeneous physical environments, Ecol. Complex., 20 (2014), 185-194.
12 S. Rana, S. Samanta, S. Bhattacharya, K. Al-Khaled, A. Goswami and J. Chattopadhyay, The effect of nanoparticles on plankton dynamics: A mathematical model, Biosystems, 127 (2015), 28-41.
13 T. G. Hallam, C. E. Clark and R. R. Lassiter, Effects of toxicants on populations: A qualitative approach I. Equilibrium environmental exposure, Ecol. Model., 18 (1983), 291-304.
14 J. T. Turner and P. A. Tester, Toxic marine phytoplankton, zooplankton grazers, and pelagic food webs, Limnol. Oceanogr., 42 (1997), 1203-1214.
15 J. Chattopadhyay, R. R. Sarkar and S. Mandal, Toxin producing plankton may act as a biological control for planktonic blooms-field study and mathematical modelling, J. Theor. Biol., 215 (2002), 333-344.
16 J. Chattopadhyay, R. R. Sarkar and A. El Abdllaoui, A delay differential equation model on harmful algal blooms in the presence of toxic substances, Math. Med. Biol., 19 (2002), 137-161.
17 R. Pal, D. Basu and M. Banerjee, Modelling of phytoplankton allelopathy with Monod-Haldane-type functional response-A mathematical study, Biosystems, 95 (2009), 243-253.
18 S. Chakraborty, S. Chatterjee, E. Venturino and J. Chattopadhyay, Recurring plankton bloom dynamics modeled via toxin-producing phytoplankton, J. Biol. Phys., 3 (2008), 271-290.
19 M. Banerjee and E. Venturino, A phytoplankton-toxic phytoplankton-zooplankton model, Ecol. Complex., 8 (2011), 239-248.
20 M. M. Mullin, E. F. Stewart and F. J. Fuglister, Ingestion by planktonic grazers as a function of concentration of food1, Limnol. Oceanogr., 20 (1975), 259-262.
21 J. B. Collings, Bifurcation and stability analysis of a temperature-dependent mite predator-prey interaction model incorporating a prey refuge, B. Math. Biol., 57 (1995), 63-76.
22 E. González-Olivares and R. Ramos-Jiliberto, Dynamic consequences of prey refuges in a simple model system: more prey, fewer predators and enhanced stability, Ecol. Model., 166 (2003), 135-146.
23 L. Chen, F. Chen and L. Chen, Qualitative analysis of a predator-rey model with Holling type II functional response incorporating a constant prey refuge, Nonlinear anal-real., 11 (2010), 246-252.       
24 T. K. Kar, Stability analysis of a prey-predator model incorporating a prey refuge, Commun. Nonlinear. Sci., 10 (2005), 681-691.       
25 Y. Huang, F. Chen and L. Zhong, Stability analysis of a prey-predator model with Holling type III response function incorporating a prey refuge, Appl. Math. Comput., 182 (2006), 672-683.       
26 D. E. Schindler and M. D. Scheuerell, Habitat coupling in lake ecosystems, Oikos, 98 (2002), 177-189.
27 P. J. Wiles, L. A. van Duren, C. Häse, J. Larsen and J. H. Simpson, Stratification and mixing in the Limfjorden in relation to mussel culture, J. Marine. Syst., 60 (2006), 129-143.
28 K. S. Cheng, S. B. Hsu and S. S. Lin, Some results on global stability of a predator-prey system, J. Math. Biol., 12 (1981), 115-126.       
29 L. P. Liou and K. S. Cheng, Global stability of a predator-prey system, J. Math. Biol., 26 (1988), 65-71.       
30 S. B. Hsu and T. W. Huang, Global stability for a class of predator-prey systems, SIAM J, Appl. Math., 55 (1995), 763-783.       
31 J. F. Talling, The annual cycle of stratification and phytoplankton growth in Lake Victoria (East Africa), Int. Revue Ges. Hydrobiol., 51 (1966), 545-621.
32 V. Lakshmikantham and S. Leela, Differential and Integral Inequalities: Theory and Applications, Academic press, 1969.
33 G. Teschl, Ordinary Differential Equations and Dynamical Systems, Am. Math. Soc., 2012.       
34 H. K. Khalil and J. W. Grizzle, Nonlinear Systems, Upper Saddle River: Prentice hall, 2000.
35 P. Lawrence, Differential Equations and Dynamical Systems, Springer-Verlag, New York, 1991.       
36 Y. A. Kuznetsov, Elements of Applied Bifurcation Theory, Spring-Verlag, New York, 1995.       

Go to top