Rocky Mountain Journal of Mathematics

Bifurcation and chaos in a pulsed plankton model with instantaneous nutrient recycling

Sanling Yuan, Yu Zhao, Anfeng Xiao, and Tonghua Zhang

Full-text: Access denied (no subscription detected) We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Article information

Source
Rocky Mountain J. Math. Volume 42, Number 4 (2012), 1387-1409.

Dates
First available: 27 September 2012

Permanent link to this document
http://projecteuclid.org/euclid.rmjm/1348752091

Digital Object Identifier
doi:10.1216/RMJ-2012-42-4-1387

Zentralblatt MATH identifier
06111471

Mathematical Reviews number (MathSciNet)
MR2981050

Subjects
Primary: 34K45: Equations with impulses 37G15: Bifurcations of limit cycles and periodic orbits 92C45: Kinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.) [See also 80A30]

Keywords
Chemostat plankton pulsed periodic solution chaos

Citation

Yuan, Sanling; Zhao, Yu; Xiao, Anfeng; Zhang, Tonghua. Bifurcation and chaos in a pulsed plankton model with instantaneous nutrient recycling. Rocky Mountain Journal of Mathematics 42 (2012), no. 4, 1387--1409. doi:10.1216/RMJ-2012-42-4-1387. http://projecteuclid.org/euclid.rmjm/1348752091.


Export citation

References

  • D.D. Bainov and P.S. Simeonov, Impulsive differential equations: Asymptotic properties of the solutions, World Scientific, 1995.
  • –––, Impulsive differential equations: Periodic solution and application, Pitman Monogr. Surv. Pure Appl. Math., 1993.
  • E. Beretta, G.I. Bischi and F. Solimano, Stability in chemostat equations with delayed nutrient recycling, J. Math. Biol. 28 (1990), 99-111.
  • S. Busenberg, S.K. Kumar, P. Austin and G. Wake, The dynamics of a model of a plankton-nutrient interaction, Bull. Math. Biol. 52 (1990), 677-696.
  • J.M. Cushing, Periodic time-dependent predator-prey systems, SIAM J. Appl. Math. 32 (1977), 82-95.
  • G. Fan and Gail S.K. Wolkowicz, Analysis of a model of nutrient driven self-cycling fermentation allowing unimodal response functions, Dynam. Contin., Discr. Impuls. Syst.: Appl. Algorithms 8 (2007), 801-831.
  • E. Funasaki and M. Kor, Invasion and chaos in periodically periodically pulsed mass-action chemostat, Theor. Popul. Biol. 44 (1993), 203-224.
  • J.K. Hale and A.S. Somolinos, Competition for fluctuating nutrient, J. Math. Biol. 18 (1983), 255-280.
  • T.G. Hallam, Controlled persistence in rudimentary plankton models. Math. Model. 4 (1977), 2081-2088.
  • V.S. Ivlev, Experimental ecology of the feeding of fishes, Yale University Press, New Haven, 1961.
  • S.R.J. Jang and J. Baglama, Persistence in variable-yield nutrient-plankton models, Math. Comp. Model. 38 (2003), 281-298.
  • B. Li and Y. Kuang, Simple food chain in a chemostat with distinct removal rates, J. Math. Anal. Appl. 242 (2000), 75-92.
  • Z. Lu and K.P. Hadeler, Model of plasmid-bearing, plasmid-free competition in the chemostat with nutrient recycling and an inhibitor, Math. Biosci. 148 (1998), 147-159.
  • P. Mayzaud and S.A. Poulet, The importance of the time factor in the response of zooplankton to varying concentrations of naturally occurring particulate matter, Limnol. Oceanogr. 23 (1978), 1144-1154.
  • B. Mukhopadhyay and R. Bhattacharyya, Modelling phytoplankton allelopathy in a nutrient-plankton model with spatial heterogeneity, Ecol. Model. 198 (2006), 163-173.
  • R.M. Nisbet, J. Mckinstry and W.S.C. Gurney, A strategic model of material cycling in a closed ecosystem, Math. Biosci. 64 (1983), 99-113.
  • S. Ruan, Persistence and coexistence in zooplankton-phytoplankton-nutrient models with instantaneous nutrient recycling, J. Math. Biol. 31 (1993), 633-654.
  • –––, Oscillations in plankton models with nutrient recycling, J. Theor. Biol. 208 (2001), 15-26.
  • H. Smith and P. Waltman, The theory of the chemostat, Cambridge University, Cambridge, UK, 1995.
  • H.L. Smith, Competitive coexistence in an oscillating chemostat, SIAM J. Appl. Math. 40 (1981), 498-522.
  • R.J. Smith and Gail S.K. Wolkowicz, Growth and competition in the nutrient driven self-cycling fermentation process, Canad. Appl. Math. Quart. 10 (2003), 171-177.
  • J.H. Steele and E.W. Henderson, The role of predation in plankton models, J. Plankton Res. 14 (1992), 157-172.
  • P.A. Taylor and J.L. Williams, Theoretical studies on the coexistence of competing species under continuous-flow conditions, Canad. J. Microbiol. 21 (1975), 90-98.
  • F. Wang, C. Hao and L. Chen, Bifurcation and chaos in a monod type food chain chemostat with pulsed input and washout, Chaos, Soliton Fract. 31 (2007), 826-839.
  • W. Wang, H. Wang and Z. Li, Chaotic behavior of a three-species Beddington-type system with impulsive perturbations, Chaos, Soliton Fract. 37 (2008), 438-443.
  • Z. Xiang and X. Song, A model of competition between plasmid-bearing and plasmid-free organisms in a chemostat with periodic input, Chaos, Soliton Fract. 32 (2007), 1419-1428.
  • S. Yuan, D. Xiao and M. Han, Competition between plasmid-bearing and plasmid-free organisms in a chemostat with nutrient recycling and an inhibitor, Math. Biosci. 202 (2006), 1-28. \noindentstyle