Asymptotic behavior of non-autonomous stochastic Gilpin–Ayala competition model with jumps

Abstract

In this paper, a non-autonomous stochastic Gilpin–Ayala competition model with jumps is studied. We show that this model has a unique global positive solution under certain conditions, and establish sufficient conditions for stochastic ultimate boundedness. Asymptotic behavior of stochastic Gilpin–Ayala competition model with jumps is also discussed. Numerical examples are introduced to illustrate the results.

Keywords:

• Gilpin–Ayala model
• jumps
• moment boundedness
• asymptotic behavior

AMS Subject Classifications:

• 34F05
• 92D25
• 60H10
• 60H20

Acknowledgements

The authors thank the editors and reviewers for their important and valuable comments. The authors also thank the National Natural Science Foundation of P.R. China (No.11171081), (No.11301207), (No.11301112), (No.11171056), (No.11001032), (No.11226254), (No.11101183), the Fundamental Research Funds for the Central Universities (No.14CX02012A).

Notes

The work was supported by the National Natural Science Foundation of P.R. China [grant number 11171081], [grant number 11301207], [grant number 11301112], [grant number 11171056], [grant number 11001032], [grant number 11226254], [grant number 11101183], the Fundamental Research Funds for the Central Universities [grant number 14CX02012A].