Ir al contenido

Documat

Stability and Bifurcation Analysis of an Amensalism Model with Weak Allee Effect

  • Wei, Zhen [1] ; Xia Yonghui [2] ; Zhang Tonghua [3]
    1. [1] Fujian Normal University

      Fujian Normal University

      China

    2. [2] Zhejiang Normal University

      Zhejiang Normal University

      China

    3. [3] Swinburne University of Technology

      Swinburne University of Technology

      Australia

    Mostrar afiliaciones +
  • Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 19, Nº 1, 2020
  • Idioma: inglés
  • DOI: 10.1007/s12346-020-00341-0
  • Enlaces
  • Resumen

    • In this paper, an amensalism model with weak Allee effect is proposed. The existence and stability of all possible positive equilibria and the possible boundary equilibria of the system are investigated. We also prove that there are two saddle-node bifurcations under suitable conditions by Sotomayor’s theorem. An example with its numeric simulations are given to verify our main results.

  • Referencias bibliográficas
    • 1. Allee, W.C.: Animal Aggregations: A Study in General Sociology. University of Chicago Press, Chicago (1931)
    • 2. Begon, M., Mortimer, M.: Population Ecology: A Unified Study of Animals and Plants. Blaekwell Scientificm, Oxford (1981)
    • 3. Chen, B.G.: Dynamic behaviors of a non-selective harvesting Lotka–Volterra amensalism model incorporating partial closure for the populations....
    • 4. Ferdy, J.B., Molofsky, J.: Allee effect, spatial structure and species coexistence. Theor. Biol. 217(4), 413–424 (2002)
    • 5. Guan, X.Y., Chen, F.D.: Dynamical analysis of a two species amensalism model with Beddington– DeAngelis functional response and Allee effect...
    • 6. Kou, K.L., Lou, Y.J., Xia, Y.H.: Zeros of a class of transcendental equation with application to bifurcation of DDE. Int. J. Bifurcat....
    • 7. Lin, Q.F., Zhou, X.Y.: On the existence of positive periodic solution of a amensalism model with Holling II functional response. Commun....
    • 8. Lin, Q.F.: Allee effect increasing the final density of the species subject to the Allee effect in a Lotka– Volterra commensal symbiosis...
    • 9. Lin, Q.F.: Stability analysis of a single species logistic model with Allee effect and feedback control. Adv. Differ. Equ. Article ID 190...
    • 10. Liu, Y., Zhao, L., Huang, X.Y., Deng, H.: Stability and bifurcation analysis of two species amensalism model with Michaelis–Menten type...
    • 11. Liu, X., Fan, G.H., Zhang, T.H.: Evolutionary dynamics of single species model with Allee effect. Phys. A Stat. Mech. Appl. 526(15), 120774...
    • 12. Mccarthy, M.A.: The Allee effect, finding mates and theoretical models. Ecol. Model. 103(1), 99–102 (1997)
    • 13. Meng, X.Z., Zhao, S.N., Feng, T., Zhang, T.H.: Dynamics of a novel nonlinear stochastic SIS epidemic model with double epidemic hypothesis....
    • 14. Perko, L.: Differential Equations and Dynamical Systems. Springer, New York (2001)
    • 15. Biswas, S.: Optimal predator control policy and weak Allee effect in a delayed prey–predator system. Nonlinear Dyn. 90(4), 2929–2957 (2017)
    • 16. Song, J., Hu,M., Bai, Y.Z., Xia, Y.H.: Dynamic analysis of a non-autonomous ratio-dependent predator– prey model with additional food....
    • 17. Song, Y.L., Jiang, H.P., Liu, Q.X., Yuan, Y.: Spatiotemporal dynamics of the diffusive Mussel–Algae model near Turing–Hopf bifurcation....
    • 18. Song, Y.L., Tang, X.S.: Stability, steady-state bifurcations and turing patterns in a predator–prey model with herd behavior and prey-taxis....
    • 19. Song, Y.L.,Wu, S.H.,Wang, H.: Spatiotemporal dynamics in the single population model with memorybased diffusion and nonlocal effect. J....
    • 20. Sun, G.C.: Qualitative analysis on two populations amensalism model. J. Jiamusi Univ. (Nat. Sci. Ed.) 21(3), 283–286 (2003)
    • 21. Tang, S.Y., Li, C.T., Tang, B., Wang, X.: Global dynamics of a nonlinear state-dependent feedback control ecological model with a multiple-hump...
    • 22. Wang, Y., Jin, Z.: Global analysis of multiple routes of disease transmission on heterogeneous networks. Phys. A Stat. Mech. Appl. 392(18),...
    • 23. Wang, M.H., Kot, M.: Speeds of invasion in a model with strong or weak Allee effects. Math. Biosci. 171(1), 83–97 (2001)
    • 24. Wang, J.F., Shi, J.P., Wei, J.J.: Predator–prey system with strong Allee effect in prey. J. Math. Biol. 62(3), 291–331 (2011)
    • 25. Wei, J.J., Li, M.Y.: Hopf bifurcation analysis in a delayed Nicholson blowflies equation. Nonlinear Anal. Theory Methods Appl. 60(7),...
    • 26. Wu, R.X., Zhao, L., Lin, Q.X.: Stability analysis of a two species amensalism model with Holling II functional response and a cover for...
    • 27. Wu, R.X.: A two species amensalism model with non-monotonic functional response. Commun. Math. Biol. Neurosci. 2016, 19 (2016)
    • 28. Xia, Y.H., Romanovski, V.G.: Bifurcation analysis of a population dynamics in a critical state. Bull. Malays. Math. Sci. Soc. 38(2), 499–527...
    • 29. Xiao, Z.W., Xie, X.D., Xue, Y.L.: Stability and bifurcation in a Holling type II predator–prey modle with Allee effect and time delay....
    • 30. Xie, X.D., Chen, F.D., He, M.X.: Dynamic behaviors of two species amensalism model with a cover for the first species. J. Math. Comput....
    • 31. Xu, C.Q., Yuan, S.L.: Competition in the chemostat: a stochastic multi-species model and its asymptotic behavior. Math. Biosci. 280, 1–9...
    • 32. Xu, F., Yu, P., Liao, X.X.: Global analysis on n-scroll chaotic attractors of modified Chua’s circuit. Int. J. Bifurcat. Chaos. 19(1),...
    • 33. Yang, J.Y., Jin, Z., Xu, F.: Threshold dynamics of an age-space structured SIR model on heterogeneous environment. Appl. Math. Lett. 96,...
    • 34. Yi, F.Q., Wei, J.J., Shi, J.P.: Diffusion-driven instability and bifurcation in the Lengyel–Epstein system. Nonlinear Anal. Real World...
    • 35. Yi, F.Q., Wei, J.J., Shi, J.P.: Bifurcation and spatiotemporal patterns in a homogeneous diffusive predater–prey system. J. Differ. Equ....
    • 36. Yu, P., Xu, F.: A common phenomenon in chaotic systems linked by time delay. Int. J. Bifurcat. Chaos. 16(12), 3727–3736 (2006)
    • 37. Yu, X.W., Yuan, S.L., Zhang, T.H.: Asymptotic properties of stochastic nutrient-plankton food chain models with nutrient recycling. Nonlinear...
    • 38. Zhang, T.H., Zhang, T.Q., Meng, X.Z.: Stability analysis of a chemostat model with maintenance energy. Appl. Math. Lett. 68, 1–7 (2017)
    • 39. Zhang, B., Zhu, W., Xia, Y., Bai, Y.: A unified analysis of exact traveling wave solutions for the fractional-order and integer-order...
    • 40. Zhang, B., Xia, Y., Zhu, W., Bai, Y.: Explicit exact traveling wave solutions and bifurcations of the generalized combined double sinh–cosh–Gordon...
    • 41. Zhang, X.G., Zhang, C.P., Jin, Z.: Structure of growing complex networks coupling with the friendship and contact relations. Chaos Solitons...
    • 42. Zhang, J.F.: Bifurcated periodic solutions in an amensalism system with strong generic delay kernel. Math. Methods Appl. Sci. 36(1), 113–124...
    • 43. Zhang, Z.: Stability and bifurcation analysis for a amensalism system with delays. Math. Numer. Sin. 30(2), 213–224 (2008)
    • 44. Zhang, Z., Ding, T.R., Huang, W.Z., Dong, Z.X.: Qualitative Theory of Differential Equation. Science Press, Beijing (1992)
    • 45. Zheng, H., Guo, L., Bai, Y.Z., Xia, Y.H.: Periodic solutions of a non-autonomous predator-prey system with migrating prey and disease...
    • 46. Zu, J., Mimura, M.: The impact of Allee effect on a predator-prey system with Holling type II functional response. Appl. Math. Comput....
Fundación Dialnet

Mi Documat

Opciones de artículo

Opciones de compartir

Opciones de entorno