Unique stationary distribution and ergodicity of a stochastic Logistic model with distributed delay

2018 ◽  
Vol 512 ◽  
pp. 864-881 ◽  
Author(s):  
Xinguo Sun ◽  
Wenjie Zuo ◽  
Daqing Jiang ◽  
Tasawar Hayat
Keyword(s):  
Stationary Distribution ◽  
Logistic Model ◽  
Distributed Delay ◽  
Stationary Distribution And Ergodicity ◽  
Stochastic Logistic Model

scholarly journals Effects of Dispersal for a Logistic Growth Population in Random Environments

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Xiaoling Zou ◽  
Dejun Fan ◽  
Ke Wang
Keyword(s):  
Stationary Distribution ◽  
Logistic Model ◽  
Numerical Experiments ◽  
Random Environments ◽  
Logistic Growth ◽  
Small Diffusion ◽  
Stochastic Logistic Model ◽  
Diffusion Rates ◽  
Definition Of ◽  
Do So

We study a stochastic logistic model with diffusion between two patches in this paper. Using the definition of stationary distribution, we discuss the effect of dispersal in detail. If the species are able to have nontrivial stationary distributions when the patches are isolated, then they continue to do so for small diffusion rates. In addition, we use some examples and numerical experiments to reflect that diffusions are capable of both stabilizing and destabilizing a given ecosystem.

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.

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