Geodesic
Dynamics of logistic systems driven by Lévy noise under regime switching
Electronic Journal of Differential Equations, Tome 2014 (2014).

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Summary: This article concerns the stochastic logistic models under regime switching with Levy noise. In the model, the color noise and Levy noise are taken into account at the same time. This model is new and more feasible and more accordance with the actual. Some dynamical behaviors are investigated and sufficient conditions for stochastic permanence, extinction, non-persistence in the mean and weak persistence are established. The critical value among the extinction, non-persistence in the mean and weak persistence is obtained. Our results demonstrate that the asymptotic properties of the model have close relations with the Levy noise and stationary distribution of the color noise.
Classification : 60H10, 60J75, 60J28
Keywords: logistic equation, Markov chain, Lévy noise, extinction, stochastic permanence 
@article{EJDE_2014__2014__a155,
     author = {Wu, Ruihua and Zou, Xiaoling and Wang, Ke},
     title = {Dynamics of logistic systems driven by {L\'evy} noise under regime switching},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2014},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2014__2014__a155/}
}
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Wu, Ruihua; Zou, Xiaoling; Wang, Ke. Dynamics of logistic systems driven by Lévy noise under regime switching. Electronic Journal of Differential Equations, Tome 2014 (2014). http://geodesic.mathdoc.fr/item/EJDE_2014__2014__a155/