Skip to main content
SpringerLink
Log in

Rhythmogenesis, birhythmicity and chaos in a metapopulation model

  • Regular Article
  • Published:
The European Physical Journal Special Topics Aims and scope Submit manuscript

Abstract

We study a mean-field coupled ecological model of metapopulation in which species from spatially fragmented habitats are connected through dispersal. The interplay between dispersal and heterogeneous characteristics of connected habitats determines the mechanisms in promoting dispersal-induced synchrony and stability of metapopulation. Depending on dispersal rate and environmental heterogeneity, the mean-field coupling acts as a feedback to the system which enables various rhythmic processes such as rhythmogenesis and birhythmicity. In addition to that, heterogeneity determines period-doubling of limit cycle which further leads to chaotic oscillation.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. L. Glass, M.C. Mackey, From Clocks to Chaos: The Rhythms of Life (Princeton University Press, Princeton, New Jersey, 1988)

  2. L. Glass, Nature (London) 410, 277 (2001)

    Article  ADS  Google Scholar 

  3. S. Reppert, D. Weaver, Nature 418, 935 (2002)

    Article  ADS  Google Scholar 

  4. U. Sommer, BioScience 35, 351 (1985)

    Article  Google Scholar 

  5. I. Hanski, Metapopulation Ecology (Oxford University Press, New York, 1999)

  6. E.E. Goldwyn, A. Hastings, Theor. Popul. Biol. 73, 395 (2008)

    Article  Google Scholar 

  7. M.D. Holland, A. Hastings, Nature (London) 456, 792 (2008)

    Article  ADS  Google Scholar 

  8. C.J. Briggs, M.F. Hoopes, Theor. Popul. Biol. 65, 299 (2004)

    Article  Google Scholar 

  9. R.E. Mirollo, S.H. Strogatz, J. Stat. Phys. 60, 245 (1990)

    Article  ADS  Google Scholar 

  10. G. Saxena, A. Prasad, R. Ramaswamy, Phys. Rep. 521, 205 (2012)

    Article  ADS  Google Scholar 

  11. A. Koseska, E. Volkov, J. Kurths, Phys. Rep. 531, 173 (2013)

    Article  ADS  MathSciNet  Google Scholar 

  12. M. Dasgupta, M. Rivera, P. Parmananda, Chaos 20, 023126 (2010)

    Article  ADS  Google Scholar 

  13. O. Decroly, A. Goldbeter, Proc. Natl. Acad. Sci. USA 79, 6917 (1982)

    Article  ADS  Google Scholar 

  14. M. Alamgir, I. Epstein, J. Am. Chem. Soc. 105, 2500 (1983)

    Article  Google Scholar 

  15. S. Kar, D.S. Ray, Europhys. Lett. 67, 137 (2004)

    Article  ADS  Google Scholar 

  16. D. Biswas, T. Banerjee, J. Kurths, Phys. Rev. E 94, 042226 (2016)

    Article  ADS  Google Scholar 

  17. M.L. Rosenzweig, R.H. MacArthur, Am. Nat. 97, 209 (1963)

    Article  Google Scholar 

  18. T. Banerjee, P.S. Dutta, A. Gupta, Phys. Rev. E 91, 052919 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  19. R. Arumugam, P.S. Dutta, T. Banerjee, Chaos 25, 103121 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  20. R. Arumugam, P.S. Dutta, T. Banerjee, Chaos 26, 123122 (2016)

    Article  MathSciNet  Google Scholar 

  21. W. Zou, D.V. Senthilkumar, R. Nagao, I.Z. Kiss, Y. Tang, A. Koseska, J. Duan, J. Kurths, Nat. Commun. 6, 7709 (2015)

    Article  ADS  Google Scholar 

  22. D. Ghosh, T. Banerjee, J. Kurths, Phys. Rev. E, 92, 052908 (2015)

    Article  ADS  Google Scholar 

  23. J.C. Allen, W.M. Schaffer, D. Rosko, Nature 364, 229 (1993)

    Article  ADS  Google Scholar 

  24. A. Hastings, C.L. Hom, S. Ellner, P. Turchin, H.C.J. Godfray, Ann. Rev. Ecol. Sys. 24, 1 (1993)

    Article  Google Scholar 

  25. B. Ermentrout, Simulating, Analyzing, and Animating Dynamical Systems: A Guide to Xppaut for Researchers and Students (Software, Environments, Tools) (SIAM Press, Philadelphia, PA, 2002)

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology, Ropar, Punjab–140 001, India

    Ramesh Arumugam & Partha Sharathi Dutta

  2. Chaos and Complex Systems Research Laboratory, Department of Physics, University of Burdwan, Rajbati, Bardhaman, West Bengal–713 104, India

    Tanmoy Banerjee

Authors
  1. Ramesh Arumugam
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Tanmoy Banerjee
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Partha Sharathi Dutta
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Tanmoy Banerjee or Partha Sharathi Dutta.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Arumugam, R., Banerjee, T. & Dutta, P.S. Rhythmogenesis, birhythmicity and chaos in a metapopulation model. Eur. Phys. J. Spec. Top. 226, 2145–2156 (2017). https://doi.org/10.1140/epjst/e2017-70017-5

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1140/epjst/e2017-70017-5

Search

Navigation