, Volume 23, Issue 4, pp 727-737
Date: 09 Sep 2010

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

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Abstract

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.

This research is supported by the Department of Science and Technology, Ministry of Human Resource Development, Govt. of India under Grant No. SR/S4/MS:296/05.