Citation: Chun Lu, Bing Li, Limei Zhou, Liwei Zhang. Survival analysis of an impulsive stochastic delay logistic model with L´evy jumps[J]. Mathematical Biosciences and Engineering, 2019, 16(5): 3251-3271. doi: 10.3934/mbe.2019162
[1] | K. Golpalsamy, Stability and oscillations in delay differential equations of population dynamics, Kluwer Academic, Dordrecht, 1992. |
[2] | K. Golpalsamy, Global asymptotic stability in Volterra's population systems, J. Math. Biol., 19 (1984), 157–168. |
[3] | Y. Kuang and H. L. Smith, Global stability for infinite delay Lotka-Valterra type systems, J. Diff. Eq.,103(1993), 221–246. |
[4] | V. B. Kolmanovskii and V. R. Nosov, Stability of functional differential equations, Academic Press, New York, 1986. |
[5] | B. Lisena, Global attractivity in nonautonomous logistic equations with delay, Nonlinear Anal.,9 (2008), 53–63. |
[6] | Y.Kuang, Delay differential equations with applications in population dynamics, AcademicPress, Boston, 1993. |
[7] | R. M. May, Stability and complexity in model ecosystems, Princeton University Press, NJ, 1973. |
[8] | T. C. Gard, Persistence in stochastic food web models, Bull. Math. Biol.,46(1984), 357–370. |
[9] | Q. Liu and D. Jiang, Stationary distribution and extinction of a stochastic predator-prey model with distributed delay, Appl. Math. Lett.,78(2018), 79–87. |
[10] | W. Mao, L. Hu and X. Mao, Neutral stochastic functional differential equations with L´evy jumps under the local Lipschitz condition, Adv. Differ. Equ.,57(2017), 1–24. |
[11] | F. Wei and K. Wang, The existence and uniquencess of the solution for stochastic functional differential equations with infinite delay, J. Math. Anal. Appl.,331(2007), 516–531. |
[12] | M.LiuandK.Wang, Global asymptotic stability of a stochastic Lotka-Volterra model with infinite delays, Commun. Nonlinear Sci. Numer. Simul.,17(2012), 3115–3123. |
[13] | M. Liu and K. Wang, Persistence and extinction in stochastic non-autonomous logistic systems, J. Math. Anal. Appl.,375(2011), 443–457. |
[14] | F. Wu and Y. Xu, Stochastic Lotka-Volterra population dynamics with infinite delay, SIAM J. Appl. Math.,70(2009), 641–657. |
[15] | M. Vasilova and M. Jovanovic, Stochastic Gilpin-Ayala competition model with infinite delay, Appl. Math. Comput.,217(2011), 4944–4959. |
[16] | C. Lu and X. Ding, Persistence and extinction in general non-autonomous logistic model with delays and stochastic perturbation, Appl. Math. Comput.,229(2014), 1–15. |
[17] | J. Bao, X. Mao, G. Yin, et al., Competitive Lotka-Volterra population dynamics with jumps, Nonlinear Anal. Theory Methods Appl.,74(2011), 6601–6616. |
[18] | M.LiuandY.Zhu, Stationarydistributionandergodicityofastochastichybridcompetitionmodel with L´evy jumps, Nonlinear Anal. Hybrid Syst.,30(2018), 225–239. |
[19] | N.H.DuandV.H.Sam, DynamicsofastochasticLotka-Volterramodelperturbedbywhitenoise, J. Math. Anal. Appl.,324(2006), 82–97. |
[20] | X. Zou and K. Wang, Numerical simulations and modeling for stochastic biological systems with jumps, Commun. Nonlinear Sci. Numer. Simul.,5(2014), 1557–1568. |
[21] | C. Lu and X. Ding, Persistence and extinction of a stochastic Gilpin-Ayala model with jumps, Math. Meth. Appl. Sci.,38(2015), 1200–1211. |
[22] | Q. Liu and Q. Chen, Analysis of a general stochastic non-autonomous logistic model with delays and L´evy jumps, J. Math. Anal. Appl.,433(2016), 95–120. |
[23] | M.Liu,J.YuandP.S.Mandal, Dynamics of a stochastic delay competitive model with harvesting and Markovian switching, Appl. Math. Comput.,337(2018), 335–349. |
[24] | M.Liu,C.DuandM.Deng, Persistence and extinction of a modified Leslie-Gower Holling-type II stochasticpredator-prey model with impulsive toxicant input in polluted environments, Nonlinear Anal.Hybrid Syst.,27(2018), 177–190. |