Seminar Event Detail


Applied Interdisciplinary Mathematics (AIM)

Date:  Friday, November 22, 2019
Location:  1084 East Hall (3:00 PM to 4:00 PM)

Title:  Harvesting of populations in stochastic environments

Abstract:   We consider the harvesting of a population in a stochastic environment whose dynamics in the absence of harvesting is described by a one dimensional diffusion. Using ergodic optimal control, we find the optimal harvesting strategy which maximizes the asymptotic yield of harvested individuals. When the yield function is the identity, we show that the optimal strategy has a bang-bang property: there exists a threshold x^*>0 such that whenever the population is under the threshold the harvesting rate must be zero, whereas when the population is above the threshold the harvesting rate must be at the upper limit. We provide upper and lower bounds on the maximal asymptotic yield, and explore via numerical simulations how the harvesting threshold and the maximal asymptotic yield change with the growth rate, maximal harvesting rate, or the competition rate. Finally, we look at the optimal harvesting strategies when one deals with a complex ecosystem of interacting species.

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Speaker:  Alex Hening
Institution:  Tufts University

Event Organizer:   Charlie Doering    doering@umich.edu

 

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