Skip to main content

Crisis-Limited Chaotic Dynamics in an Eco-epidemiological System of the Salton Sea

  • Conference paper
  • 1731 Accesses

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 283))

Abstract

In this paper, we have proposed a new eco-epidemiological model of the Salton Sea with Holling type II & IV functional responses. Numerical results are presented in the form of phase portraits, 2D scans, bifurcation analysis and basin boundary calculations. By these we have concluded that model system depicts the short-term recurrent chaos (STRC) and argued that crisis-limited chaotic dynamics can be commonly found in model eco-epidemiological systems.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Lotka, A.J.: Elements of Physical Biology. Williams and Wilkins Co., Inc., Baltimore (1924)

    MATH  Google Scholar 

  2. Volterra, V.: Variazioni e Fluttuazioni del Numero d’individui in Specie Animali Conviventi. Mem. R. Accad. Naz. Dei Lincei. 2, 31–113 (1926)

    MATH  Google Scholar 

  3. Kermack, W.O., McKendrick, A.G.: A Contribution to the Mathematical Theory of Epdidemics. Pro. Royal Soc. London, A 115, 700–721 (1727)

    Google Scholar 

  4. Anderson, R.M., May, R.M.: The Invasion, Persistence, and Spread of Infectious Diseases within Animal and Plant Communities. Philos. Trans. R. Soc. Lond. B 314, 533–570 (1986)

    Article  Google Scholar 

  5. Chattopadhyay, J., Arino, O.: A Predator-Prey Model with Disease in the Prey. Nonlin. Analys. Theo. Meth. Appl. 36, 747–766 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  6. Packer, C., Holt, R.D., Hudson, P.J., Lafferty, K.D., Dobson, A.P.: Keeping the Herds Healthy and Alert: Implications of Predator Control for Infectious Disease. Ecol. Lett. 6, 792–802 (2003)

    Article  Google Scholar 

  7. Grebogi, C., Ott, E., Yorke, J.A.: Chaotic Attractor in Crisis. Phys. Rev. Lett. 42, 1507–1510 (1982)

    Article  MathSciNet  Google Scholar 

  8. Grebogi, C., Ott, E., Yorke, J.A.: Crises, Sudden Changes in Chaotic Attractors, and Transient Chaos. Physica 7D, 181–200 (1983)

    MathSciNet  MATH  Google Scholar 

  9. Dangoisse, D., Glorieux, P., Hennequin, D.: Laser Chaotic in Crisis. Phys. Rev. Lett. 57, 2657–2660 (1986)

    Article  Google Scholar 

  10. Chattopadhyay, J., Srinivasu, P.D.N., Bairagi, N.: Pelicans at Risk in Salton Sea - An Eco-epidemiological Model-II. Ecol. Model 167, 199–211 (2003)

    Article  Google Scholar 

  11. Chattopadhyay, J., Bairagi, N.: Pelicans at Risk in Salton Sea - An Eco-epidemiological Model. Ecol. Model 136, 103–112 (2001)

    Article  Google Scholar 

  12. Upadhyay, R.K., Bairagi, N., Kundu, K., Chattopadhyay, J.: Chaos in Eco-epidemiological Problem of the Salton Sea and its Possible Control. Appl. Math. Comp. 196, 392–401 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  13. Andrews, J.F.: A Mathematical Model for the Continuous Culture of Microorganisms Utilizing Inhibitory Substrates. Biotech. Bioeng. 10, 707–723 (1968)

    Article  Google Scholar 

  14. Upadhyay, R.K., Raw, S.N.: Complex Dynamics of a Three Species Food-Chain Model with Holling type IV Functional Response. Nonlin. Anal. Model. Cont. 16, 353–374 (2011)

    MathSciNet  MATH  Google Scholar 

  15. Holling, C.S.: The Response of Predators to Prey Density and its Role in Mimicry and Population Regulation. Mem. Ent. Soc. Can. 45, 1–60 (1965)

    Google Scholar 

  16. Nusse, H.E., Yorke, J.A.: Dynamics: Numerical Exploration. Springer, NY (1994)

    Book  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Raw, S.N., Upadhyay, R.K., Thakur, N.K. (2012). Crisis-Limited Chaotic Dynamics in an Eco-epidemiological System of the Salton Sea. In: Balasubramaniam, P., Uthayakumar, R. (eds) Mathematical Modelling and Scientific Computation. ICMMSC 2012. Communications in Computer and Information Science, vol 283. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28926-2_21

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-28926-2_21

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-28925-5

  • Online ISBN: 978-3-642-28926-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics