Dr. Sampurna Sengupta
Assistant Professor
My general research interests lie in the area of mathematical modeling. My research problems involve mathematical modeling of ecological systems as well as dynamical analysis of these problems analytically and numerically. I have tried to find out the effects of environmental fluctuation and human-initiated disturbance on some population models with Holling type-III functional response. The focus of my research is on two major areas of mathematical modeling: stochastic dynamical systems and optimal control problems.
1. Stochastic dynamical systems: To analyze the survival conditions of threatened species, some prey-predator population has been formulated with white noise terms. It is proved that fluctuating environment plays a crucial role in the survival of species by comparing the stochastic models with deterministic models. I have analyzed the existence of a global positive solution, persistence, permanence, and extinction of the stochastic models.
For example, in one of my papers, a stochastic model has been formulated for the system with polar bear preying on ringed and bearded seals. The impact of climate change on the intrinsic growth terms and carrying capacities of prey and predator populations have been thoroughly investigated in this stochastic system. The threshold criteria between persistence and extinction of the polar bear have been established. Analytical results prove that populations can sustain over a very long period of time if the intensity of fluctuation is low, which has also been verified numerically. Also, the stochastic and deterministic systems, good and bad climate days have been compared numerically in this work.
2. Optimal control: Since fishes and squids are very popular among the human population for food items, so they get hugely harvested by fishermen. Some control mechanisms have been suggested which can protect the endangered species from extinction as well as safeguard economic sustainability. Where it is not possible to control the disturbance, I have discussed the other ways to save the population from extinction.
For example, in one of my papers, the aquatic two-prey one-predator model in international waters has been considered with harvesting and toxicity effect. Specifically, orange roughy is the predator, preying on prawns and small fishes. Because no one can restrict harvesting in international waters, we need some other way to protect these species from extinction. The findings show preserving a portion of prey-predator separately without harvesting and toxicity can help these threatened species to sustain. The sufficient conditions of the permanence and extinction of the species in a partially closed system have derived. The optimal value of the reserved portion has been obtained for which total profit gets maximized while predator orange roughy sustain in the future for long time.