Geodesic
Modeling the role of constant and time varying recycling delay on an ecological food chain
Applications of Mathematics, Tome 55 (2010) no. 3, pp. 221-240.

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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.
DOI : 10.1007/s10492-010-0009-5
Classification : 34C25, 34D23, 34K13, 34K18, 34K20, 34K60, 92D25, 92D40
Keywords: autotroph; herbivore; nutrient recycling; global stability; Hopf-bifurcation; variable delay; two-timing expansion 
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     title = {Modeling the role of constant and time varying recycling delay on an ecological food chain},
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Mukhopadhyay, Banibrata; Bhattacharyya, Rakhi. Modeling the role of constant and time varying recycling delay on an ecological food chain. Applications of Mathematics, Tome 55 (2010) no. 3, pp. 221-240. doi : 10.1007/s10492-010-0009-5. http://geodesic.mathdoc.fr/articles/10.1007/s10492-010-0009-5/

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