Alternative Attractors and Regime Shift in a Stochastic Logistic Model

2010 ◽  
Author(s):  
Jianfeng Feng ◽  
Lin Zhu ◽  
Weiqing Meng ◽  
Hongli Wang
Keyword(s):  
Logistic Model ◽  
Regime Shift ◽  
Stochastic Logistic Model

On the Extinction of the S–I–S stochastic logistic epidemic

1989 ◽  
Vol 26 (04) ◽  
pp. 685-694
Author(s):  
Richard J. Kryscio ◽  
Claude Lefèvre
Keyword(s):  
Chemical Reactions ◽  
Logistic Model ◽  
Diffusion Processes ◽  
Birth And Death Processes ◽  
Time To Extinction ◽  
Stochastic Logistic Model ◽  
Mean Time To Extinction ◽  
The Mean ◽  
Mean Time ◽  
Quasi Stationary Distribution

We obtain an approximation to the mean time to extinction and to the quasi-stationary distribution for the standard S–I–S epidemic model introduced by Weiss and Dishon (1971). These results are a combination and extension of the results of Norden (1982) for the stochastic logistic model, Oppenheim et al. (1977) for a model on chemical reactions, Cavender (1978) for the birth-and-death processes and Bartholomew (1976) for social diffusion processes.

An optimal hunting policy for a stochastic logistic model

1979 ◽  
Vol 16 (2) ◽  
pp. 319-331 ◽  
Author(s):  
Andris Abakuks
Keyword(s):  
Population Growth ◽  
Population Size ◽  
Optimal Policy ◽  
Logistic Model ◽  
Stochastic Version ◽  
Stochastic Logistic Model ◽  
Parameter Values

A stochastic version of the logistic model for population growth is considered, and the general form of an optimal policy is found for hunting the population so as to maximise the long-term average number of captures per unit time. This optimal policy is described by a critical population size x∗such that it is optimal to hunt if and only if the population size is greater than or equal to x∗. Methods of determining x∗for given parameter values are provided, and some properties of the optimal policy as the population size tends to infinity are proved.

An optimal hunting policy for a stochastic logistic model

1979 ◽  
Vol 16 (02) ◽  
pp. 319-331 ◽  
Author(s):  
Andris Abakuks
Keyword(s):  
Population Growth ◽  
Population Size ◽  
Optimal Policy ◽  
Logistic Model ◽  
Stochastic Version ◽  
Stochastic Logistic Model ◽  
Parameter Values

A stochastic version of the logistic model for population growth is considered, and the general form of an optimal policy is found for hunting the population so as to maximise the long-term average number of captures per unit time. This optimal policy is described by a critical population size x∗such that it is optimal to hunt if and only if the population size is greater than or equal to x∗. Methods of determining x∗for given parameter values are provided, and some properties of the optimal policy as the population size tends to infinity are proved.

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