Analysis and control of pre-extinction dynamics in stochastic populations
Autor: | Nieddu, Garrett, Billings, Lora, Forgoston, Eric |
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Rok vydání: | 2014 |
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Druh dokumentu: | Working Paper |
Popis: | We consider a stochastic population model where the intrinsic or demographic noise causes cycling between states before the population eventually goes extinct. A master equation approach coupled with a WKB (Wentzel-Kramers-Brillouin) approximation is used to construct the optimal path to extinction. In addition, a probabilistic argument is used to understand the pre-extinction dynamics and approximate the mean time to extinction. Analytical results agree well with numerical Monte Carlo simulations. A control method is implemented to decrease the mean time to extinction. Analytical results quantify the effectiveness of the control and agree well with numerical simulations. Comment: 17 pages, 9 figures. Final version to appear in Bulletin of Mathematical Biology |
Databáze: | arXiv |
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