Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
권호 표지

EFFECT OF TIME DELAY IN AN AUTOTROPH-HERBIVORE SYSTEM WITH NUTRIENT CYCLING

  • Das, Kalyan (Center for Mathematical Biology and Ecology Department of Mathematics jadavpur University) ;
  • Sarkar, A.K. (Center for Mathematical Biology and Ecology Department of Mathematics jadavpur University)
  • Published : 1998.09.01

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Abstract

In the present study we consider a mathematical model of a non-interactive type autotroph-herbivore system in which the amount of autotroph biomass consumed by the herbivore is assumed to follow a Holling type II functional response. We have also incorpo-rated discrete time delays in the numerical response term to represent a delay due to gestation and in the recycling term which represent a delay due to gestation and in the recycling term which represents the time required for bacterial decomposition. We have derived con-dition for global asymptotic stability of the model in the absence of delays. Conditions for delay-induced asymptotic stability of the steady state are also derived. The length of the delay preserving stability has been estimated and interpreted ecologically.

Keywords

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