Persistence and extinction of a modified Leslie–Gower Holling-type II two-predator one-prey model with Lévy jumps

References

• W. Abid, R. Yafia, M.A. Aziz-Alaoui, and A. Aghriche, Dynamics analysis and optimality in selective harvesting predator–prey model with modified Leslie–Gower and Holling-type II, Nonauton. Dyn. Syst. 6 (2019), pp. 1–17.
   Google Scholar
• N. Ali and M. Jazar, Global dynamics of a modified Leslie–Gower predator–prey model with Crowley–Martin functional responses, Appl. Math. Comput. 43 (2013), pp. 271–293.
   Google Scholar
• D. Applebaum, Lévy Processes and Stochastics Calculus, 2nd ed., Cambridge University Press, New York, 2009.
   Google Scholar
• M.A. Aziz-Alaoui and M.D. Okiye, Boundedness and global stability for a predator–prey model with modified Leslie–Gower and Holling-type II schemes, Appl. Math. Lett. 16 (2003), pp. 1069–1075.
   Web of Science ®Google Scholar
• M. Banerjee and S. Banerjee, Turing instabilities and spatio-temporal chaos in ratio-dependent Holling–Tanner model, Math. Biosci. 236 (2012), pp. 64–76.
   PubMed Web of Science ®Google Scholar
• J. Bao and C. Yuan, Stochastic population dynamics driven by Lévy noise, J. Math. Anal. Appl. 391 (2012), pp. 363–375.
   Web of Science ®Google Scholar
• J. Bao, X. Mao, G. Yin, and C. Yuan, Competitive Lotka–Volterra population dynamics with jumps, Nonlinear Anal. 74 (2011), pp. 6601–6616.
   Web of Science ®Google Scholar
• J.R. Beddington and R.M. May, Harvesting natural populations in a randomly fluctuating environment, Science 197 (1977), pp. 463–465.
   PubMed Web of Science ®Google Scholar
• Y. Cai, J. Jiao, Z. Gui, Y. Liu, and W. Wang, Environmental variability in a stochastic epidemic model, Appl. Math. Comput. 329 (2018), pp. 210–226.
   Web of Science ®Google Scholar
• J. Cao and R. Yuan, Bifurcation analysis in a modified Leslie–Gower model with Holling type II functional response and delay, Nonlinear Dyn. 84 (2016), pp. 1341–1352.
   Web of Science ®Google Scholar
• F. Chen, L. Chen, and X. Xie, On a Leslie–Gower predator–prey model incorporating a prey refuge, Nonlinear Anal. Real World Appl. 10 (2009), pp. 2905–2908.
   Web of Science ®Google Scholar
• R.K. Ghaziania, J. Alidousti, and A.B. Eshkaftaki, Stability and dynamics of a fractional order Leslie–Gower prey–predator model, Appl. Math. Model. 40 (2016), pp. 2075–2086.
   Web of Science ®Google Scholar
• X. Guan, W. Wang, and Y. Cai, Spatiotemporal dynamics of a Leslie–Gower predator–prey model incorporating a prey refuge, Nonlinear Anal. Real World Appl. 12 (2011), pp. 2385–2395.
   Web of Science ®Google Scholar
• H. Guo and X. Song, An impulsive predator–prey system with modified Leslie–Gower and Holling type II schemes, Chaos Solitons Fractals 36 (2008), pp. 1320–1331.
   Web of Science ®Google Scholar
• C. Ji, D. Jiang, and 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), pp. 482–498.
   Web of Science ®Google Scholar
• C. Ji, D. Jiang, and N. Shi, A note on a predator–prey model with modified Leslie–Gower and Holling-type II schemes with stochastic perturbation, J. Math. Anal. Appl. 377 (2011), pp. 435–440.
   Web of Science ®Google Scholar
• D. Jiang and N. Shi, A note on non-autonomous logistic equation with random perturbation, J. Math. Anal. Appl. 303 (2005), pp. 164–172.
   Web of Science ®Google Scholar
• H. Kunita, Itô's stochastic calculus: its surprising power for applications, Stoch. Process. Appl. 120 (2010), pp. 622–652.
   Web of Science ®Google Scholar
• X. Li and X. Mao, Population dynamical behavior of non-autonomous Lotka–Volterra competitive system with random perturbation, Discrete Contin. Dyn. Syst. 24 (2009), pp. 523–545.
   Web of Science ®Google Scholar
• R.S. Lipster, A strong law of large numbers for local martingales, Stochastics 3 (1980), pp. 217–228.
   Google Scholar
• M. Liu, Dynamics of a stochastic regime-switching predator–prey model with modified Leslie–Gower Holling-type II schemes and prey harvesting, Nonlinear Dyn. 96 (2019), pp. 417–442.
   Web of Science ®Google Scholar
• M. Liu and C. Bai, Dynamics of a stochastic one-prey two-predator model with Lévy jumps, Appl. Math. Comput. 284 (2016), pp. 308–321.
   Web of Science ®Google Scholar
• M. Liu, K. Wang, and Q. Wu, Survival analysis of stochastic competitive models in a polluted environment and stochastic competitive exclusion principle, Bull. Math. Biol. 73 (2011), pp. 1969–2012.
   PubMed Web of Science ®Google Scholar
• M. Liu, C. Du, and M. Deng, Persistence and extinction of a modified Leslie–Gower Holling-type II stochastic predator–prey model with impulsive toxicant input in polluted environments, Nonlinear Anal. Hybrid Syst. 27 (2018), pp. 177–190.
   Web of Science ®Google Scholar
• X. Mao and C. Yuan, Stochastic Differential Equations with Markovian Switching, Imperial College Press, London, 2006
   Google Scholar
• L. Nie, Z. Teng, L. Hu, and J. Peng, Qualitative analysis of a modified Leslie–Gower and Holling-type II predator–prey model with state dependent impulsive effects, Nonlinear Anal. Real World Appl. 11 (2010), pp. 1364–1373.
   Web of Science ®Google Scholar
• A.F. Nindjin, M.A. Aziz-Alaoui, and M. Cadivel, Analysis of a predator–prey model with modified Leslie–Gower and Holling-type II schemes with time delay, Nonlinear Anal. Real World Appl. 7 (2006), pp. 1104–1118.
   Web of Science ®Google Scholar
• S. Peng and X. Zhu, Necessary and sufficient condition for comparison theorem of 1-dimensional stochastic differential equations, Stoch. Process. Appl. 116 (2006), pp. 370–380.
   Web of Science ®Google Scholar
• P. Protter and D. Talay, The Euler scheme for Lévy driven stochastic differential equations, Ann. Probab. 25 (1997), pp. 393–423.
   Web of Science ®Google Scholar
• X. Song and Y. Li, Dynamic behaviors of the periodic predator–prey model with modified Leslie–Gower Holling-type II schemes and impulsive effect, Nonlinear Anal. Real World Appl. 9 (2008), pp. 64–79.
   Web of Science ®Google Scholar
• Y. Tian and P. Weng, Stability analysis of diffusive predator–prey model with modified Leslie–Gower and Holling-type III schemes, Appl. Math. Comput. 218 (2011), pp. 3733–3745.
   Web of Science ®Google Scholar
• Y. Xu, M. Liu, and Y. Yang, Analysis of a stochastic two-predators one-prey system with modified Leslie–Gower and Holling-type II schemes, J. Appl. Anal. Comput. 7 (2017), pp. 713–727.
   Google Scholar
• R. Yafia, F. Adnani, and H. Alaoui, Limit cycle and numerical simulations for small and large delays in a predator–prey model with modified Leslie–Gower and Holling-type II schemes, Nonlinear Anal. Real World Appl. 9 (2008), pp. 2055–2067.
   Web of Science ®Google Scholar
• Y. Zhao, S. Yuan, and J. Ma, Survival and stationary distribution analysis of a stochastic competitive model of three species in a polluted environment, Bull. Math. Biol. 77 (2015), pp. 1285–1326.
   PubMed Web of Science ®Google Scholar
• J. Zhou, C. Kim, and J. Shi, Positive steady state solutions of a diffusive Leslie–Gower predator–prey model with Holling type II functional response and cross-diffusion, Discrete Contin. Dyn. Syst. 34 (2014), pp. 3875–3899.
   Web of Science ®Google Scholar
• D. Zhou, M. Liu, and Z. Liu, Persistence and extinction of a stochastic predator–prey model with modified Leslie–Gower and Holling-type II schemes, Adv. Differ. Equ. 1 (2020), pp. 1–15.
   Google Scholar
• X. Zou, D. Fan, and K. Wang, Stationary distribution and stochastic Hopf bifurcation for a predator–prey system with noises, Discrete Contin. Dyn. Syst. Ser. B 18 (2013), pp. 1507–1519.
   Web of Science ®Google Scholar