A note on a predator-prey model with modified Leslie-Gower and Holling-type II schemes with stochastic perturbation

Journal of Mathematical Analysis and Applications

Volumn 377, Issue 1, 2011, Pages 435-440

  Ji, Chunyan ^a,b   Jiang, Daqing ^a   Shi, Ningzhong ^a  

^a NORTHEAST NORMAL UNIVERSITY   (China)

^b CHANGSHU INSTITUTE OF TECHNOLOGY   (China)

Author keywords

Ergodicity; It formula; Stationary distribution

Indexed keywords

EID: 78651240619     PISSN: 0022247X     EISSN: 10960813     Source Type: Journal    
DOI: 10.1016/j.jmaa.2010.11.008     Document Type: Article

References (9)

1. Atar R., Budhiraja A., Dupuis P. On positive recurrence of constrained diffusion processes. Ann. Probab. 2001, 29:979-1000.
2. Aziz-Alaoui M.A., Daher Okiye M. Boundedness and global stability for a predator-prey model with modified Leslie-Gower and Holling-type II schemes. Appl. Math. Lett. 2003, 16:1069-1075.
3. Gard T.C. Introduction to Stochastic Differential Equations 1988, Madison Avenue 270, New York.
4. Hasminskii R.Z. Stochastic stability of differential equations. Monogr. Textb. Mech. Solids Fluids 1980, vol. 7. Sijthoff & Noordhoff, Alphen aan den Rijn, The Netherlands.
5. Ji C.Y., Jiang D.Q., Shi N.Z. Analysis of a predator-prey model with modified Leslie-Gower and Holling-type II schemes with stochastic perturbation. J. Math. Anal. Appl. 2009, 359:482-498.
6. Kliemann W. Recurrence and invariant measures for degenerate diffusions. Ann. Probab. 1987, 15:690-707.
7. Mao X., Yuan C., Zou J. Stochastic differential delay equations of population dynamics. J. Math. Anal. Appl. 2005, 304:296-320.
8. Strang G. Linear Algebra and Its Applications 1988, Thomson Learning, Inc.
9. Zhu C., Yin G. Asymptotic properties of hybrid diffusion systems. SIAM J. Control Optim. 2007, 46:1155-1179.