Stochastic permanence and extinction of a hybrid predator-prey system with jumps

[1] D. Applebaum, Levy Processes and Stochastic Calculus, 2nd ed. Cambridge University Press, 2009.
[2] A. Bahar, X. Mao, Stochastic delay population dynamics, Int. J. Pure Appl. Math. 11 (2004) 377–
400.
[3] J. Bao, X. Mao, G. Yin, C. Yuan, Competitive Lotka-Volterra population dynamics with jumps,
Nonlinear Anal. 74 (2011) 6601–6616.
[4] J. Bao, C. Yuan, Stochastic population dynamics driven by Levy noise, J. Math. Anal. Appl. 391
(2012) 363–375.
[5] N. Du, V. Sam, Dynamics of a stochastic Lotka-Volterra model perturbed by white noise, J. Math.
Anal. Appl. 324 (2006) 82–97.
[6] D. Higham, An algorithmic introduction to numerical simulation of stochastic differential equa-
tions, SIAM Rev. 43 (2001) 525–546.
[7] Y. Hu, F. Wu, C. Huang, Stochastic Lotka-Volterra models with multiple delays, J. Math. Anal.
Appl. 375 (2011) 42–57.
[8] C. Ji, D. Jiang, N. Shi, Analysis of a predator-prey model with modified Leslie-Gower and Holling-
type II schemes with stochastic perturbation, J. Math. Anal. Appl. 359 (2009) 482–498.
[9] D. Jiang, C. Ji, X. Li, D. O’Regan, Analysis of autonomous Lotka-Volterra competition systems
with random perturbation, J. Math. Anal. Appl. 390 (2012) 582–595.
[10] X. Li, A. Gray, D. Jiang, X. Mao, Sufficient and necessary conditions of stochastic permanence
and extinction for stochastic logistic populations under regime switching, J. Math. Anal. Appl. 376
(2011) 11–28.
[11] X. Li, X. Mao, Population dynamical behavior of non-autonomous Lotka-Volterra competitive sys-
tem with random perturbation, Discrete Contin. Dyn. Syst. 24 (2009) 523–545.
[12] M. Liu, M. Deng, B. Du, Analysis of a stochastic logistic model with diffusion, Appl. Math. Comput.
266 (2015) 169–182.
[13] M. Liu, K. Wang, Analysis of a stochastic autonomous mutualism model, J. Math. Anal. Appl. 402
(2013) 392–403.
[14] M. Liu, K. Wang, Dynamics of a Leslie-Gower Holling-type II predator-prey system with Levy
jumps, Nonlinear Anal. 85 (2013) 204–213.

[15] M. Liu, K. Wang, Stochastic Lotka-Volterra systems with Levy noise, J. Math. Anal. Appl. 410
(2014) 750–763.
[16] Q. Luo, X. Mao, Stochastic population dynamics under regime switching, J. Math. Anal. Appl. 334
(2007) 69–84.
[17] Q. Luo, X. Mao, Stochastic population dynamics under regime switching II, J. Math. Anal. Appl.
355 (2009) 577–593.
[18] J. Lv, K. Wang, Asymptotic properties of a stochastic predator-prey system with Holling II func-
tional response, Commun. Nonlinear Sci. Numer. Simulat. 16 (2011) 4037–4048.
[19] X. Mao, S. Sabanis, E. Renshaw, Asymptotic behavior of the stochastic Lotka-Volterra model, J.
Math. Anal. Appl. 287 (2003) 141–156.
[20] X. Mao, G. Yin, C. Yuan, Stabilization and destabilization of hybrid systems of stochastic differen-
tial equations, Automatica 43, 264-273 (2007)
[21] X. Mao, C. Yuan, Stochastic Differential Equations with Markovian Switching, Imperial College
Press, London, 2006.
[22] M. Ouyang, X. Li, Permanence and asymptotical behavior of stochastic prey-predator system with
Markovian switching, Appl. Math. Comput. 266 (2015) 539–559.
[23] Y. Takeuchi, N. Du, N. Hieu, K. Sato, Evolution of predator-prey systems described by a Lotka-
Volterra equation under random environment, J. Math. Anal. Appl. 323 (2006) 938–957.
[24] L. Wan, Q. Zhou, Stochastic Lotka-Volterra model with infinite delay, Statist. Probab. Lett. 79
(2009) 698–706.
[25] X. Zhang, W. Li, M. Liu, K. Wang, Dynamics of a stochastic Holling II one-predator two-prey
system with jumps, Physica A 421 (2015) 571–582.
[26] X. Zhang, X. Zou, K. Wang, Dynamics of Stochastic Holling II Predator-Prey under Markovian-
Switching with Jumps, Filomat 29 (2015) 1925–1940.
[27] C. Zhu, G. Yin, On competitive Lotka-Volterra model in random environments, J. Math. Anal. Appl.
357 (2009) 154–170.
[28] C. Zhu, G. Yin, On hybrid competitive Lotka-Volterra ecosystems, Nonlinear Anal. 71 (2009) 1370–
1379.
[29] X. Zou, K. Wang, Optimal harvesting for a stochastic regime-switching logistic diffusion system
with jumps, Nonlinear Anal. Hybrid Syst. 13 (2014) 32–44.