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

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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.

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Authors and Affiliations

  1. Department of Science, Central Calcutta Polytechnic, 21, Convent Road, Kolkata, 700 014, India

    Banibrata Mukhopadhyay

  2. Department of Science, The Calcutta Technical School, 110, S.N. Banerjee Road, Kolkata, 700 013, India

    Rakhi Bhattacharyya

Authors
  1. Banibrata Mukhopadhyay
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  2. Rakhi Bhattacharyya
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Correspondence to Banibrata Mukhopadhyay.

Additional information

The present research is performed under a project supported by the Department of Science and Technology, Ministry of Human Resource Development, Govt. of India (Grant No. SR/S4/MS:296/05).

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Mukhopadhyay, B., Bhattacharyya, R. Modeling the role of constant and time varying recycling delay on an ecological food chain. Appl Math 55, 221–240 (2010). https://doi.org/10.1007/s10492-010-0009-5

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