A note on migration perturbation and convergence rates to a steady state
Автор: Blume Lawrence Edward, Lukina Aleksandra Andreevna
Журнал: Программные системы: теория и приложения @programmnye-sistemy
Рубрика: Методы оптимизации и теория управления
Статья в выпуске: 4 (47) т.11, 2020 года.
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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.
The leslie population model, migration perturbation, convergence rates to a steady state
Короткий адрес: https://sciup.org/143174569
IDR: 143174569 | DOI: 10.25209/2079-3316-2020-11-4-17-30
Список литературы A note on migration perturbation and convergence rates to a steady state
- C. Meyer. Matrix Analysis and Applied Linear Algebra, SIAM, 2000, , 718 pp. ISBN: 0-89871-454-0
- E. Seneta. Non-Negative Matrices and Markov Chains, 2nd ed., Springer-Verlag, New York, 1981, 978-0-387-29765-1, 281 pp. DOI: 10.1007/0-387-32792-4 ISBN: 978-0-387-29765-1
- H. Caswell. Matrix Population Models: Construction, Analysis, and Interpretation, 2nd ed., Sinauer Associates, Inc., 2001, , 722 pp. ISBN: 0-87893-096-5
- Y. Svirezhev, D. Logofet. Stability of Biological Communities, Mir, M., 1978, , 352 pp. (in Russian). ISBN: 0-8285-2371-1
- D. A. Levin, Y. Peres, E. L. Wilmer. Markov Chains and Mixing Times, AMS, 2009, 978-1-4704-2962-1, 371 pp. ISBN: 978-1-4704-2962-1
- B. E. Kendall, M. Fujiwara, J. Diaz-Lopez, S. Schneider, J. Voigt, S. Wiesner. “Persistent problems in the construction of matrix population models”, Ecological modelling, 406 (2019), pp. 33--43. DOI: 10.1016/j.ecolmodel.2019.03.011
- E. Behrends. Introduction to Markov Chains with Special Emphasis on Rapid Mixing, Vieweg-Verlag, 2000, 978-3-528-06986-5, 234 pp. DOI: 10.1007/978-3-322-90157-6 ISBN: 978-3-528-06986-5