Journal of Systems Science and Complexity

, Volume 23, Issue 4, pp 727–737

Role of different system delays on ecological food chain dynamics: Mathematical modelling and analysis


DOI: 10.1007/s11424-010-8190-x

Cite this article as:
Bhattacharyya, R., Bera, A. & Mukhopadhyay, B. J Syst Sci Complex (2010) 23: 727. doi:10.1007/s11424-010-8190-x


This paper studies a three tier ecological food chain model consisting of nutrient, autotroph, and herbivore populations. Regeneration of nutrient from dead autotroph and herbivore biomass by decomposers present in the soil is included. The time required for maturation of the herbivore population is incorporated as a distributed time delay. Next, the authors introduce the time lag required for regeneration of nutrient from the dead herbivore as a discrete time delay. Stability and bifurcation behavior of the one- and two-delay models are carried out and a comparative study of the significance of these delays in controlling the system dynamics is performed. Numerical simulations are done to justify analytical results.

Key words

Autotrophdecomposergestation delayherbivorehopf bifurcationrecycling delay

Copyright information

© Institute of Systems Science, Academy of Mathematics and Systems Science, CAS and Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • R. Bhattacharyya
    • 1
  • Ashoke Bera
    • 1
  • B. Mukhopadhyay
    • 2
  1. 1.Department of Sciencethe Calcutta Technical SchoolKolkataIndia
  2. 2.Department of ScienceCentral Calcutta PolytechnicKolkataIndia