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Stochastic two-species mutualism model with jumps
Volume 7, Issue 1 (2020), pp. 1–15
Olga Borysenko   Oleksandr Borysenko  

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https://doi.org/10.15559/20-VMSTA150
Pub. online: 3 March 2020      Type: Research Article      Open accessOpen Access

Received
3 December 2019
Revised
21 February 2020
Accepted
21 February 2020
Published
3 March 2020

Abstract

The existence and uniqueness are proved for the global positive solution to the system of stochastic differential equations describing a two-species mutualism model disturbed by the white noise, the centered and non-centered Poisson noises. We obtain sufficient conditions for stochastic ultimate boundedness, stochastic permanence, nonpersistence in the mean, strong persistence in the mean and extinction of the solution to the considered system.

References

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Borysenko, O.D., Borysenko, D.O.: Asymptotic Behavior of the Solution to the Non-Autonomous Stochastic Logistic Differential Equation. Theory Probab. Math. Stat. 2(101), 40–48 (2019)
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Li, M., Gao, H., Wang, B.: Analysis of a non-autonomous mutualism model driven by Lévy jumps. Discrete Contin. Dyn. Syst., Ser. B 21(4), 1189–1202 (2016). MR3483558. https://doi.org/10.3934/dcdsb.2016.21.1189
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Qiu, H., Lv, J., Wang, K.: Two types of permanence of a stochastic mutualism model. Adv. Differ. Equ. 2013, 37 (2013). http://www.advancesindifferenceequations.com/content/2013/1/37. MR3033721. https://doi.org/10.1186/1687-1847-2013-37

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Keywords
Stochastic mutualism model global solution stochastic ultimate boundedness stochastic permanence extinction nonpersistence in the mean strong persistence in the mean

MSC2010
92D25 60H10 60H30

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