[1] HSU S B, HWANG T W, KUANG Y. A ratio-dependent food chain model and its applications to biological control[J]. Math Biosci, 2003, 181: 55-83. [2] 李海红.随机种群模型的渐进行为[D].长春:吉林大学, 2014. [3] SUN Y, SAKER S H. Positive periodic solutions of discrete three-level food-chain model of Holling type Ⅱ[J]. Appl Math Comput, 2006, 180: 353-365. [4] GOH B S. Global stability in many-species systems[J] The American Naturalist, 1977, 111(977): 135-143. [5] LIU M, BAI C. Analysis of a stochastic tri-trophic food-chain model with harvesting[J]. J Math Biol, 2016, 73: 597-625. [6] BAO J, YUAN C. Stochastic population dynamics driven by Lévy noise[J]. J Math Anal Appl, 2012, 391: 363-375. [7] LI M, GAO H, WANG B. Analysis of a non-autonomous mutualism model driven by Lévy jumps[J]. Discrete & Continuous Dynamical Systems - B, 2016, 21(4): 1189-1202. [8] LIU M, WANG K. Stochastic Lotka-Volterra systems with Lévy noise[J]. J Math Anal Appl, 2014, 410: 750-763. [9] LIU M, BAI C. Dynamics of a stochastic one-prey two-predator model with Lévy jumps[J]. Appl Math Comput, 2016, 284: 308-321. [10] LIU Q, JIANG D, SHI N. Stochastic mutualism model with Lévy jumps[J]. Comm Nonl Sci Num Simul, 2016, 43: 78-90. [11] ZHOU Y, YUAN S, ZHAO D. Threshold behavior of a stochastic SIS model with Lévy jumps[J]. Appl Math Comput, 2016, 275: 255-267. [12] GE Q, JI G, XU J, et al. Extinction and persistence of a stochastic nonlinear SIS epidemic model with jumps[J]. Physica A: Statistical Mechanics and Its Applications, 2016, 462: 1120-1127. [13] CHEN C, KANG Y. Dynamics of a stochastic multi-strain SIS epidemic model driven by Lévy noise[J]. Comm Nonl Sci Num Simul, 2017, 42: 379-395. [14] MAO W, MAO X. On the asymptotic stability and numerical analysis of solutions to nonlinear stochastic differential equations with jumps[J]. J Comput Appl Math, 2016, 301: 1-15. [15] ZOU X,WANG K. Numerical simulations and modeling for stochastic biological systems with jumps[J]. Comm Nonl Sci Nume Simul, 2014, 19: 1557-1568. [16] ZHANG X, WANG K. Stability analysis of a stochastic Gilpin-Ayala model driven by Lévy noise[J]. Comm Nonl Sci Nume Simul, 2014, 19(5): 1391-1399. [17] WU R, ZOU X, WANG K. Asymptotic properties of stochastic hybrid Gilpin-Ayala system with jumps[J]. Appl Math Comput, 2014, 249: 53-66. [18] JIANG D, SHI N, LI X. Global stability and stochastic permanence of a non-autonomous logistic equation with random perturbation[J]. J Math Anal Appl, 2008, 340: 588-597. [19] LIPTSER R S. A strong law of large numbers for local martingales[J]. Stoch Inter J Prob Stoch Proc, 1980, 3: 217-228. [20] MAO X, MARION G, RENSHAW E. Environmental Brownian noise suppresses explosions in population dynamics[J]. Stoch Proc Appl, 2002, 97: 95-110.
() () |