Dynamical analysis on stochastic two-species models

References

• Cailly P, Tran A, Balenghien T, et al. A climate driven abundance model to assess mosquito control strategies. Ecol Modell. 2012;227:7–17. doi: 10.1016/j.ecolmodel.2011.10.027
   Web of Science ®Google Scholar
• Huang MG, Luo JW, Hu LC, et al. Assessing the efficiency of Wolbachia driven Aedes mosquito suppression by delay differential equations. J Theor Biol. 2018;440:1–11. doi: 10.1016/j.jtbi.2017.12.012
   PubMed Web of Science ®Google Scholar
• May BM. Stability and complexity in model ecosystems. IEEE Trans Syst Man Cybern. 1976;SMC-6(12):887–887. doi: 10.1109/TSMC.1976.4309488
   Google Scholar
• Gard TC. Persistence in stochastic food web models. Bull Math Biol. 1984;46(3):357–370. doi: 10.1016/S0092-8240(84)80044-0
   Web of Science ®Google Scholar
• Liu M, Wang K. Persistence and extinction in stochastic non-autonomous logistic systems. J Math Anal Appl. 2011;375(2):443–457. doi: 10.1016/j.jmaa.2010.09.058
   Web of Science ®Google Scholar
• Mandal PS, Banerjee M. Stochastic persistence and stationary distribution in a Holling-Tanner type prey-predator model. Physica A Stat Mech Appl. 2012;391(4):1216–1233. doi: 10.1016/j.physa.2011.10.019
   Web of Science ®Google Scholar
• Zou XL, Fan DJ, Wang K. Stationary distribution and stochastic Hopf bifurcation for a predator-prey system with noises. Discrete Continuous Dyn Syst Ser B. 2013;18(5):1507–1519. doi: 10.3934/dcdsb.2013.18.1507
   Web of Science ®Google Scholar
• Xiong JJ, Li X, Wang H. Global asymptotic stability of a Lotka-Volterra competition model with stochasticity in inter-specific competition. Appl Math Lett. 2019;89:58–63. doi: 10.1016/j.aml.2018.09.018
   Web of Science ®Google Scholar
• Sun ZR, Lv JL, Zou XL. Dynamical analysis on two stochastic single-species models. Appl Math Lett. 2020;99:Article ID 105982.
   Web of Science ®Google Scholar
• Cai YM, Mao XR. Analysis of a stochastic predator-prey system with foraging arena scheme. Appl Math Model. 2018;64:357–371. doi: 10.1016/j.apm.2018.07.034
   Web of Science ®Google Scholar
• Majumder A, Adak D, Bairagi N. Phytoplankton-zooplankton interaction under environmental stochasticity: survival, extinction and stability. Appl Math Model. 2021;89:1382–1404. doi: 10.1016/j.apm.2020.06.076
   Web of Science ®Google Scholar
• Liu YF, Jiao F, Hu LC. Modeling mosquito population control by a coupled system. J Math Anal Appl. 2021;506:Article ID 125671.
   Web of Science ®Google Scholar
• N'Zi E, N'Zi M. Extinction and stationary distribution of a stochastic SIRS epidemic model incorporating media coverage. J Adv Math Comput. 2019;36:1–9.
   Google Scholar
• Zhao Y, Yuan SL, Ma JL. Survival and stationary distribution analysis of a stochastic competitive model of three species in a polluted environment. Bull Math Biol. 2015;77(7):1285–1326. doi: 10.1007/s11538-015-0086-4
   PubMed Web of Science ®Google Scholar
• Li XH, Lu C, Zhang LJ. Survival analysis of a traditional competition system with stochastic perturbation research. Math Pract Theory. 2016;46:171–179.
   Google Scholar
• Zhou YL, Zhang WG, Yuan SL. Survival and stationary distribution of a SIR epidemic model with stochastic perturbations. Appl Math Comput. 2014;244:118–131.
   Web of Science ®Google Scholar
• Zu L, Jiang DQ, O'Regan D, et al. Dynamic analysis of a stochastic toxin-mediated predator-prey model in aquatic environments. J Math Anal Appl. 2021;41:Article ID 125424.
   Google Scholar
• Gikhman II, Skorokhod AV. Stochastic differential equations. Berlin: Springer; 1972.
   Google Scholar
• Liu SJ, Liu MX. Extinction and stationary distribution of a random SIQR epidemic model. Math Pract Theory. 2021;51:149–155.
   Google Scholar
• Korobeinikov A, Shaikhet L. Global asymptotic properties of a stochastic model of population growth. Appl Math Lett. 2021;12:Article ID 107429.
   Google Scholar
• Qi HK, Meng XZ. Stationary distribution of a stochastic predator-prey model with hunting cooperation. Appl Math Lett. 2022;124:Article ID 107662. doi: 10.1016/j.aml.2021.107662
   Web of Science ®Google Scholar
• Neal P. Stochastic and deterministic analysis of SIS household epidemics. Adv Appl Probab. 2006;38(4):943–968. doi: 10.1239/aap/1165414587
   Web of Science ®Google Scholar
• Xiao MD, Ruan SG. Global dynamics of a ratio-dependent predator-prey system. J Math Biol. 2001;43(3):268–290. doi: 10.1007/s002850100097
   PubMed Web of Science ®Google Scholar
• Xing ZJ, Cui HC, Zhang JM. Dynamics of a stochastic intraguild predation model. Appl Sci. 2016;6(4):118. doi: 10.3390/app6040118
   Google Scholar
• Srinivas MN, Kumar GB, Madhusudanan V. Dynamics of a prey predator disease model with Holling type functional response and stochastic perturbation. Adv Math. 2020;9:471–488.
   Google Scholar
• Hua C. Analysis on the dynamics behavior of a rumor transmission model with stochastic perturbation. Bull Sci Technol. 2016;53:39–45.
   Google Scholar
• Wang F, Wang S, Peng YF. Asymptotic behavior of multigroup SEIR model with nonlinear incidence rates under stochastic perturbations. Discrete Dyn Nat Soc. 2020;333:1–12.
   Google Scholar
• Beretta E, Kolmanovskii V, Shaikhet L. Stability of epidemic model with time delays influenced by stochastic perturbations. Math Comput Simul. 1998;45(3-4):269–277. doi: 10.1016/S0378-4754(97)00106-7
   Web of Science ®Google Scholar
• Mao XR, Marion G, Renshaw E. Environmental Brownian noise suppresses explosions in population dynamics. Stoch Process Their Appl. 2002;97(1):95–110. doi: 10.1016/S0304-4149(01)00126-0
   Web of Science ®Google Scholar
• Hasminskii RZ. Stochastic stability of differential equations. Alphen aan denRijn, The Netherlands (MD): Sijthoff & Noordhoff; 1980.
   Google Scholar
• Lahrouz A, Omari L, Kiouach D, et al. Deterministic and stochastic stability of a mathematical model of smoking. Stat Probab Lett. 2011;81(8):1276–1284. doi: 10.1016/j.spl.2011.03.029
   Web of Science ®Google Scholar
• Yin GG, Zhu C. Hybrid switching diffusions: properties and applications. New York (NY): Springer; 2010.
   Google Scholar
• Higham DJ. An algorithmic introduction to numerical simulation of stochastic differential equations. SIAM Rev. 2001;43(3):525–546. doi: 10.1137/S0036144500378302
   Web of Science ®Google Scholar