Methods for Optimal Control and Control Theory

Article # 18_2020

14 p.

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Lawrence E. Blume, Aleksandra A. Lukina
A Note on Migration Perturbation and Convergence Rates to a Steady State

Using tools developed in the Markov chains literature, we study convergence times in the Leslie population model in the short and middle run. Assuming that the population is in a steady-state and reproduces itself period after period, we address the following question: how long will it take to get back to the steady-state if the population distribution vector was affected by some shock as, for instance, the “brain drain”? We provide lower and upper bounds for the time required to reach a given distance from the steady-state.

Key words: The Leslie population model, migration perturbation, convergence rates to a steady-state.

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