Modeling the role of constant and time varying recycling delay on an ecological food chain

Banibrata Mukhopadhyay; Rakhi Bhattacharyya

Applications of Mathematics (2010)

  • Volume: 55, Issue: 3, page 221-240
  • ISSN: 0862-7940

Abstract

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We consider a mathematical model of nutrient-autotroph-herbivore interaction with nutrient recycling from both autotroph and herbivore. Local and global stability criteria of the model are studied in terms of system parameters. Next we incorporate the time required for recycling of nutrient from herbivore as a constant discrete time delay. The resulting DDE model is analyzed regarding stability and bifurcation aspects. Finally, we assume the recycling delay in the oscillatory form to model the daily variation in nutrient recycling and deduce the stability criteria of the variable delay model. A comparison of the variable delay model with the constant delay one is performed to unearth the biological relevance of oscillating delay in some real world ecological situations. Numerical simulations are done in support of analytical results.

How to cite

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Mukhopadhyay, Banibrata, and Bhattacharyya, Rakhi. "Modeling the role of constant and time varying recycling delay on an ecological food chain." Applications of Mathematics 55.3 (2010): 221-240. <http://eudml.org/doc/37845>.

@article{Mukhopadhyay2010,
abstract = {We consider a mathematical model of nutrient-autotroph-herbivore interaction with nutrient recycling from both autotroph and herbivore. Local and global stability criteria of the model are studied in terms of system parameters. Next we incorporate the time required for recycling of nutrient from herbivore as a constant discrete time delay. The resulting DDE model is analyzed regarding stability and bifurcation aspects. Finally, we assume the recycling delay in the oscillatory form to model the daily variation in nutrient recycling and deduce the stability criteria of the variable delay model. A comparison of the variable delay model with the constant delay one is performed to unearth the biological relevance of oscillating delay in some real world ecological situations. Numerical simulations are done in support of analytical results.},
author = {Mukhopadhyay, Banibrata, Bhattacharyya, Rakhi},
journal = {Applications of Mathematics},
keywords = {autotroph; herbivore; nutrient recycling; global stability; Hopf-bifurcation; variable delay; two-timing expansion; autotroph; herbivore; nutrient recycling; global stability; Hopf-bifurcation; variable delay; two-timing expansion},
language = {eng},
number = {3},
pages = {221-240},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Modeling the role of constant and time varying recycling delay on an ecological food chain},
url = {http://eudml.org/doc/37845},
volume = {55},
year = {2010},
}

TY - JOUR
AU - Mukhopadhyay, Banibrata
AU - Bhattacharyya, Rakhi
TI - Modeling the role of constant and time varying recycling delay on an ecological food chain
JO - Applications of Mathematics
PY - 2010
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 55
IS - 3
SP - 221
EP - 240
AB - We consider a mathematical model of nutrient-autotroph-herbivore interaction with nutrient recycling from both autotroph and herbivore. Local and global stability criteria of the model are studied in terms of system parameters. Next we incorporate the time required for recycling of nutrient from herbivore as a constant discrete time delay. The resulting DDE model is analyzed regarding stability and bifurcation aspects. Finally, we assume the recycling delay in the oscillatory form to model the daily variation in nutrient recycling and deduce the stability criteria of the variable delay model. A comparison of the variable delay model with the constant delay one is performed to unearth the biological relevance of oscillating delay in some real world ecological situations. Numerical simulations are done in support of analytical results.
LA - eng
KW - autotroph; herbivore; nutrient recycling; global stability; Hopf-bifurcation; variable delay; two-timing expansion; autotroph; herbivore; nutrient recycling; global stability; Hopf-bifurcation; variable delay; two-timing expansion
UR - http://eudml.org/doc/37845
ER -

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