Dynamical analysis of a modified Leslie–Gower Holling-type II predator-prey stochastic model in polluted environments with interspecific competition and impulsive toxicant input

References

• 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
• C. Bai, Multiplicity of solutions for a class of nonlocal elliptic operators systems, Bull. Korean Math. Soc. 54 (2017), pp. 715–729.
   Web of Science ®Google Scholar
• J.H. Bao, X.R. Mao, G. Yin, and C.G. Yuan, Competitive Lotka–Volterra population dynamics with jumps, Nonlinear Anal. Real World Appl. 74 (2011), pp. 6601–6616.
   Google Scholar
• J.R. Beddington, Mutual interference between parasites or predators and its effect on searching efficiency, J. Anim. Ecol. 44 (1975), pp. 331–340.
   Web of Science ®Google Scholar
• B. Buonomo, A.D. Liddo, and I. Sgura, A diffusive-convective model for the dynamics of population-toxicant intentions: Some analytical and numerical results, Math. Biosci. 157 (1999), pp. 37–64.
   PubMed Web of Science ®Google Scholar
• Y.L. Cai, J.J. Jiao, Z.J. Gui, Y.T. Liu, and W.M. Wang, Environmental variability in a stochastic epidemic model, Appl. Math. Comput. 329 (2018), pp. 210–226.
   Web of Science ®Google Scholar
• H.I. Freedman and J.B. Shukla, Models for the effect of toxicant in single-species and predator-prey systems, J. Math. Biol. 30 (1991), pp. 15–30.
   PubMed Web of Science ®Google Scholar
• Y.X. Gao and S.y. Yao, Persistence and extinction of a modified Leslie–Gower Holling-type II predator-prey stochastic model in polluted environments with impulsive toxicant input, Math. Biosci. Eng. 18 (2021), pp. 4894–4918.
   PubMed Web of Science ®Google Scholar
• T.G. Hallam, C.E. Clark, and G.S. Jordan, Effffects of toxicant on population: A qualitative approach II. First order kinetics, J. Math. Biol. 109 (1983), pp. 411–429.
   Google Scholar
• T.G. Hallam, C.E. Clark, and R.R. Lassiter, Effects of toxicants on populations: A qualitative approach I. Equilibrium environmental exposure, Ecol. Model. 8 (1983), pp. 291–304.
   Web of Science ®Google Scholar
• T.G. Hallam and J.L. Deluna, Effffects of toxicant on populations: A qualitative approach III. Environmental and food chain pathways, J. Theor. Biol. 109 (1984), pp. 411–429.
   Web of Science ®Google Scholar
• T.G. Hallam and Z. Ma, Persistence in population models with demographic fluctuations, J. Math. Biol. 24 (1986), pp. 327–339.
   PubMed Web of Science ®Google Scholar
• Q.X. Han, D.Q. Jiang, and C.Y. Ji, Analysis of a delayed stochastic predator-prey model in a polluted environment, Appl. Math. Model. 38 (2014), pp. 3067–3080.
   Web of Science ®Google Scholar
• D.J. Higham, An algorithmic introduction to numerical simulation of stochastic differential equations, J. Siam Rev. 43(3) (2001), pp. 525–546.
   Web of Science ®Google Scholar
• N. Ikeda and S. Wantanabe, Stochastic Differential Equations and Diffusion Processes, North-Holland, Amsterdam, 1981.
   Google Scholar
• A.L. Jensen and S.J. Marshall, Application of a surplus production model to assess environmental impacts on exploited populations of daphnia pulex in the laboratory, J. Environ. Pollut. 28 (1982), pp. 273–280.
   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.Q. Jiang and N.Z. 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
• E.L. Johnston and M.J. Keough, Field assessment of effects of timing and frequency of copper pulses on settlement of sessile marine invertebrates, Mar. Biol. 137 (2000), pp. 1017–1029.
   Web of Science ®Google Scholar
• E.L. Johnston, M.J. Keough, and P.Y. Qian, Maintenance of species dominance through pulse disturbances to a sessile marine invertebrate assemblage in port shelter, Mar. Ecol. Prog. Ser. 226 (2002), pp. 103–114.
   Web of Science ®Google Scholar
• J. Liang, S. Tang, J.J. Nieto, and R.A. Cheke, Analytical methods for detecting pesticide switches with evolution of pesticide resistance, Math. Biosci. 245 (2013), pp. 249–257.
   PubMed Web of Science ®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.Z. Bai, Persistence and extinction of a stochastic cooperative model in a polluted environment with pulse toxicant input, Filomat 29 (2015), pp. 1329–1342.
   Web of Science ®Google Scholar
• Q. Liu and Q.M. Chen, Dynamics of stochastic delay Lotka–Volterra systems with impulsive toxicant input and Lévy noise in polluted environments, Appl. Math. Comput. 256 (2015), pp. 52–67.
   Web of Science ®Google Scholar
• B. Liu, L. Chen, and Y. Zhang, The effects of impulsive toxicant input on a population in a polluted environment, J. Biol. Syst. 11 (2003), pp. 265–274.
   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, J. Nonlinear Anal. Hybrid. Syst. 27 (2018), pp. 177–190.
   Web of Science ®Google Scholar
• H. Liu and Z. Ma, The threshold of survival for system of two species in a polluted environment, J. Math. Biol. 30 (1991), pp. 49–51.
   PubMed Web of Science ®Google Scholar
• M. Liu and K. Wang, Dynamics of a Leslie–Gower Holling-type II predator-prey system with Lévy jumps, Nonlinear Anal. 85 (2013), pp. 204–213.
   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
• B. Liu and L. Zhang, Dynamics of a two-species Lotka–Volterra competition system in a polluted environment with pulse toxicant input, Appl. Math. Comput. 214 (2009), pp. 155–162.
   Web of Science ®Google Scholar
• Z. Ma and T.G. Hallam, Effects of parameter fluctuations on community survival, Math. Biosci. 86 (1987), pp. 35–49.
   Web of Science ®Google Scholar
• R.M. May, Stability and Complexity in Model Ecosystems, Princeton University Press, Princeton (NJ), 2001.
   Google Scholar
• A. Nelson-SmithThe Problem of Oil Pollution of the Sea, Academic Press, 1971.
   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. RWA 7 (2006), pp. 1104–1118.
   Google Scholar
• J. Pan, Z. Jin, and Z. Ma, Thresholds of survival for an n-dimensional volterra mutualistic system in a polluted environment, J. Math. Anal. Appl. 252 (2000), pp. 519–531.
   Web of Science ®Google Scholar
• J.B. Shukla, I.H. Freedman, V.M.. Pal, O.P.. Misra, M. Agarwal, and A. Shukla, Degradation and subsequent regeneration of a forestry resource: A mathematical model, J. Ecol. Modell. 44 (1989), pp. 219–229.
   Web of Science ®Google Scholar
• G.T. Skalski and J.F. Gilliam, Functional responses with predator interference: Viable alternatives to the Holling type II model, Ecology 82 (2001), pp. 3083–3092.
   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. RWA 9 (2008), pp. 64–79.
   Google Scholar
• F.Y. Wei, S.A.H. Geritz, and J.Y. Cai, A stochastic single-species population model with partial pollution tolerance in a polluted environment, Appl. Math. Lett. 63 (2017), pp. 130–136.
   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
• X. Yang, Z. Jin, and Y. Xue, Weak average persistence and extinction of a predator-prey system in a polluted environment with impulsive toxicant input, Chaos Solit. Fractals 31 (2007), pp. 726–735.
   Web of Science ®Google Scholar
• S.W. Zhang and D.J. Tan, Dynamics of a stochastic predator-prey system in a polluted environment with pulse toxicant input and impulsive perturbations, Appl. Math. Model. 39 (2015), pp. 6319–6331.
   Web of Science ®Google Scholar
• W.C. Zhao, J. Li, T.Q. Zhang, X.Z. Meng, and T.H. Zhang, Persistence and ergodicty of plant disease model with Markov conversion and impulsive toxicant input, Commun. Nonlinear Sci. Numer. Simul. 48 (2017), pp. 70–84.
   Web of Science ®Google Scholar
• Y. Zhao, S.L. Yuan, and J.L. 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