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A mathematical model describing the thyroid-pituitary axis with time delays in hormone transportation

Banibrata MukhopadhyayRakhi Bhattacharyya — 2006

Applications of Mathematics

In the present paper, a mathematical model, originally proposed by Danziger and Elmergreen and describing the thyroid-pituitary homeostatic mechanism, is modified and analyzed for its physiological and clinical significance. The influence of different system parameters on the stability behavior of the system is discussed. The transportation delays of different hormones in the bloodstream, both in the discrete and distributed forms, are considered. Delayed models are analyzed regarding the stability...

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

Banibrata MukhopadhyayRakhi Bhattacharyya — 2010

Applications of Mathematics

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...

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