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Stochastic Dynamics of a Two-Species Patch-System With Ratio-Dependent Functional Response

  • Zhao, Xin [1] ; Zeng, Zhijun [1]
    1. [1] Northeast Normal University

      Northeast Normal University

      China

  • Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 21, Nº 3, 2022
  • Idioma: inglés
  • Enlaces
  • Resumen
    • In this paper, we analyze the features of a stochastically perturbed two-species predator-prey patch-system with ratio-dependent functional response. We first prove that the system which we investigate has a unique global positive solution. Then, the sufficient criteria for the existence and uniqueness of an ergodic stationary distribution of positive solutions to the system are presented by establishing a series of suitable Lyapunov functions.

  • Referencias bibliográficas
    • 1. Arditi, R., Salah, H.: Empirical evidence of the role of heterogeneity in ratio-dependent consumption. Ecology 73, 1544–1551 (1992)
    • 2. Arditi, R., Ginzburg, L.R., Akcakaya, H.R.: Variation in plankton densities among lakes: a case for ratio-dependent models. Am. Nat. 138,...
    • 3. Arditi, R., Perrin, N., Saiah, H.: Functional response and heterogeneities: an experiment test with clado-cerans. OIKOS 60, 69–75 (1991)
    • 4. Gutierrez, A.P.: The physiological basis of ratio-dependent predator-prey theory: a methbolic pool model of Nicholson’s blowflies as an...
    • 5. Li, Z., Chen, L., Huang, J.: Permanence and periodicity of a delayed ratio-dependent predator-prey model with Holling type functional response...
    • 6. Hanski, I.: The functional response of predator: worries bout scale. TREE 6, 141–142 (1991)
    • 7. Dolman, P.M.: The intensity of interference varies with resource density: evidence from a field study with snow buntings, Plectrophenax...
    • 8. Jost, C., Arditi, R.: From pattern to process: identifying predator-prey models from time-series data. Popul. Ecol. 43, 229–243 (2001)
    • 9. Skalski, G.T., Gilliam, J.F.: Functional responses with predator interference: viable alternatives to the Holling type II model. Ecology...
    • 10. Gao, X., Ishag, S., Fu, S., Li, W., Wang, W.: Bifurcation and Turing pattern formation in a diffusive ratio-dependent predator-prey model...
    • 11. Zhang, X., Liu, Z.: Periodic oscillations in age-structured ratio-dependent predator-prey model with Michaelis-Menten type functional...
    • 12. Arditi, R., Ginzburg, L.R.: Coupling in predator-prey dynamics: ratio-dependence. J. Theor. Biol. 139, 311–326 (1989)
    • 13. Jorné, J., Safriel, U.N.: Linear and non-linear diffusion models applied to the behavior of a population of an intertidal snail. J. Theor....
    • 14. Liu, M., Deng, M., Du, B.: Analysis of a stochastic logistic model with diffusion. Appl. Math. Comput. 228, 141–146 (2014)
    • 15. Gramlich, P., Plitzko, S.J., Rudolf, L., Drossel, B., Gross, T.: The influence of dispersal on a predatorprey system with two habitats....
    • 16. Kang, Y., Kumar Sasmal, S., Messan, K.: A two-patch prey-predator model with predator dispersal driven by the predation strength. Math....
    • 17. Xu, R., Chen, L.: Persistence and stability for a two-species ratio-dependent predator-prey system with time delay in a two-patch environment....
    • 18. Kumar, A.: Rajeev: a moving boundary problem with space-fractional diffusion logistic population model and density-dependent dispersal...
    • 19. Freedman, H.I., Takeuchi, Y.: Predator survial versus extinction as a function of dispersal in a predatorprey model with pacthy environment....
    • 20. Huang, R., Wang, Y., Wu, H.: Population abundance in predator-prey systems with predator’s dispersal between two patches. Theor. Popul....
    • 21. Cui, J., Takeuchi, Y., Lin, Z.: Permanence and extinction for dispersal population systems. J. Math. Anal. Appl. 298, 73–93 (2004)
    • 22. Sasmal, S.K., Ghosh, D.: Effect of dispersal in two-patch prey-predator system with positive density dependence growth of preys. BioSystems...
    • 23. Zhang, S., Zhang, T., Yuan, S.: Dynamics of a stochastic predator-prey model with habitat complexity and prey aggregation. Ecol. Complex....
    • 24. May, R.M.: Stability and Complexity in Model Ecosystems. Princeton University Press, NJ (2001)
    • 25. Pimentel, C.E.H., Rodriguez, P.M., Valencia, L.A.: A note on a stage-specific predator-prey stochastic model. Phys. A 553, 124575 (2020)
    • 26. Feng, T., Meng, X., Zhang, T., et al.: Analysis of the predator-prey interactions: a stochastic model incorporating disease invasion....
    • 27. Wang, Z., Deng, M., Liu, M.: Stationary distribution of a stochastic ratio-dependent predator-prey system with regime-switching. Chaos...
    • 28. Zou, X., Lv, J., Wu, Y.: A note on a stochastic Holling-II predator-prey model with a prey refuge. J. Frankl. Inst. Eng. Appl. Math. 357,...
    • 29. Liu, C., Wang, L., He, D., Li, M.: Stochastic dynamical analysis in a hybrid bioeconomic system with telephone noise and distributed delay....
    • 30. Roy, J., Barman, D., Alam, S.: Role of fear in a predator-prey system with ratio-dependent functional response in deterministic and stochastic...
    • 31. Ren, Y., Sakthivel, R.: Stochastic differential equations with perturbations driven by G-Brownian motion. Qual. Theory Dyn. Syst. 19,...
    • 32. Liu, Q., Jiang, D., Hayat, T., Ahmad, B.: Stationary distribution and extinction of a stochastic predatorprey model with additional food...
    • 33. Mao, X.: Stochastic Differential Equations and Applications. Horwood Publishing, Chichester (1997)
    • 34. Zhao, X., Zeng, Z.: Stationary distribution and extinction of a stochastic ratio-dependent predator-prey system with stage structure for...
    • 35. Qi, H., Leng, X., Meng, X., et al.: Periodic solution and ergodic stationary distribution of SEIS dynamical systems with active and latent...
    • 36. Liu, Y., Xu, H., Li, W.: Intermittent control to stationary distribution and exponential stability for hybrid multi-stochastic-weight...
    • 37. Higham, D.J.: An algorithmic introduction to numerical simulation of stochastic differential equations. SIAM Rev. 43, 525–546 (2001)
    • 38. Khasminskii, R.: Stochastic Stability of Differential Equations. Springer, Heidelberg Dordrecht London, New York (2012)

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