Dynamic Analysis of a Discrete Amensalism Model with Additive Allee Effect on the First Population

• Yuting Huang ^[1] ; Fengde Chen ^[1] ; Lijuan Chen ^[1] ; Zhong Li ^[1]
  1. [1] Fuzhou University

     Fuzhou University

     China

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 25, Nº 1, 2026
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • Existing discrete amensalism models often overlook intraspecific density dependence.

    This paper introduces an additive Allee effect to construct a novel discrete-time amensalism system, aiming to reveal its profound impact on population dynamics. The study reveals that under a weak Allee effect, population persistence requires maintaining the population size above a critical survival threshold; whereas a strong Allee effect leads to the extinction of the amensal population without impacting the other.

    The research elucidates a complete dynamic transition pathway from "coexistence" through "bistability" to eventual "extinction," providing a key theoretical basis for the conservation of population susceptible to Allee effects in amensalistic systems.

• Referencias bibliográficas
  • 1. Veiga, J.P.: Commensalism, amensalism, and synnecrosis, in Encyclopedia of Evolutionary Biology, Academic Press, 322–328 (2016)
  • 2. Xi, X., Griffin, J.N., Sun, S.: Grasshoppers amensalistically suppress caterpillar performance and enhance plant biomass in an alpine meadow....
  • 3. Townsend, H.M., Huyvaert, K.P., Hodum, P.J., Anderson, D.J.: Nesting distributions of Galápagos boobies (Aves: Sulidae): an apparent case...
  • 4. Osakabe, M., Hongo, K., Funayama, K., Osumi, S.: Amensalism via webs causes unidirectional shifts of dominance in spider mite communities....
  • 5. Akimoto, S.: Coexistence and weak amensalism of congeneric gall-forming aphids on the Japanese elm. Popul. Ecol. 37(1), 81–89 (1995)
  • 6. Sun, G.: Qualitative analysis on two populations amensalism model. J. Jiamusi Univ. 21, 283–286 (2003)
  • 7. Guan, X., Chen, F.: Dynamical analysis of a two species amensalism model with Beddington-DeAngelis functional response and Allee effect...
  • 8. Guo, X., Ding, L., Hui, Y., Song, X.: Dynamics of an amensalism system with strong Allee effect and nonlinear growth rate in deterministic...
  • 9. He, X., Zhu, Z., Chen, J., Chen, F.: Dynamical analysis of a Lotka-Volterra commensalism model with additive Allee effect. Open Math. 20,...
  • 10. Lin, Q., Zhou, X.: On the existence of positive periodic solution of a amensalism model with Holling-II functional response. Commun. Math....
  • 11. Luo, D., Wang, Q.: Global dynamics of a Holling-II amensalism system with nonlinear growth rate and Allee effect on the first species....
  • 12. Luo, D., Wang, Q.: Global dynamics of a Beddington–DeAngelis amensalism system with weak Allee effect on the first species. Appl. Math....
  • 13. Wei, Z., Xia, Y., Zhang, T.: Stability and bifurcation analysis of an amensalism model with weak Allee effect. Qual. Theory Dyn. Syst....
  • 14. Zhao, M., Du, Y.: Stability and bifurcation analysis of an amensalism system with Allee effect. Adv. Difference Equ. 2020, 1–13 (2020)
  • 15. Zhou, Q., Chen, F., Lin, S.: Complex dynamics analysis of a discrete amensalism system with a cover for the first species. Axioms 11(8),...
  • 16. Chen, J., He, X., Chen, F.: The influence of fear effect to a discrete-time predator-prey system with predator has other food resource....
  • 17. Zhu, Q., Chen, F., Li, Z., Chen, L.: Global dynamics of two-species amensalism model with BeddingtonDeAngelis functional response and...
  • 18. Schreiber, S.: Allee effects, extinctions, and chaotic transients in simple population models. Theor. Popul. Biol. 64, 201–209 (2003)
  • 19. Courchamp, F., Clutton-Brock, T., Grenfell, B.: Inverse density dependence and the Allee effect. Trends Ecol. Evol 14, 405–410 (1999)
  • 20. García, C., Rendueles, M., Díaz, M.: Microbial amensalism in Lactobacillus casei and Pseudomonas taetrolens mixed culture. Bioprocess...
  • 21. Zhou, Q., Chen, F.: Dynamical analysis of a discrete amensalism system with the BeddingtonDeAngelis functional response and Allee effect...
  • 22. Zhou, Q., Chen, Y., Chen, S., Chen, F.: Dynamic analysis of a discrete amensalism model with Allee effect. J. Appl. Anal. Comput. 13,...
  • 23. Hu, X., Li, H., Chen, F.: Bifurcation analysis of a discrete amensalism model. Int. J. Bifurcat. Chaos 34(02), 2450020 (2024)
  • 24. Dennis, B.: Allee effects: population growth, critical density, and the chance of extinction. Nat. Resour. Model. 3(4), 481–538 (1989)
  • 25. Wei, Z., Xia, Y., Zhang, T.: Stability and bifurcation analysis of a commensal model with additive Allee effect and nonlinear growth rate....
  • 26. Huang, X., Chen, L., Xia, Y., Chen, F.: Dynamical analysis of a predator–prey model with additive Allee effect and migration. J. Bifurcat....
  • 27. Zhu, Q., Li, Z., Chen, F.: Bifurcation in a single-species logistic model with addition Allee effect and fear effect-type feedback control....
  • 28. Wang, S., Xie, Z., Zhong, R., Wu, Y.: Stochastic analysis of a predator-prey model with modified Leslie-Gower and Holling type II schemes....
  • 29. Wang, S., Wang, Z., Xu, C., Jiao, G.: Sensitivity analysis and stationary probability distributions of a stochastic two-prey one-predator...
  • 30. Tripathi, J.P., Meghwani, S.S., Thakur, M., Abbas, S.: A modified Leslie-Gower predator-prey interaction model and parameter identifiability....
  • 31. Li, Q., Chen, F., Chen, L., Li, Z.: Dynamical analysis of a discrete amensalism system with MichaelisMenten type harvesting for the second...
  • 32. Elaydi, S.N.: An Introduction to Difference Equations, 3rd edn. Springer, New York (2005)
  • 33. Luo, D., Qiu, Y.: Global dynamics of a Holling-II amensalism system with a strong Allee effect on the harmful species. Int. J. Bifurcat....
  • 34. Wu, R.: Dynamic behaviors of a nonlinear amensalism model. Adv. Difference Equ. 2018, 1–13 (2018)
  • 35. Singh, M.K., Sharma, A.: Analysis of qualitative behaviour of two-species amensalism model under constant-yield harvesting. AIP Conf....
  • 36. Singh, M.K.: Dynamical study and optimal harvesting of a two-species amensalism model incorporating nonlinear harvesting. Applications...
  • 37. Li, T., Wang, Q.: Bifurcation analysis for two-species commensalism (amensalism) systems with distributed delays. Int. J. Bifurcat. Chaos...
  • 38. Ibrahim, M.: Global stability and bifurcation analysis of a Holling type II amensalism model with harvesting: an optimal control approach....
  • 39. Liu, X., Liu, M.: Dynamical analysis of an amensalism system with the impulsive harvesting. Advances in Differential Equations & Control...
  • 40. Chong, Y., Chen, F.: Global stability, bifurcations and chaos control in a discrete amensalism model with cover and saturation effect....
  • 41. Liu, Y., Zhao, L., Huang, X., Deng, H.: Stability and bifurcation analysis of two species amensalism model with Michaelis-Menten type...
  • 42. Tripathi, J.P., Bhuria, S., Yadav, S., Tiwari, S.K., Tripathi, D., Tiwari, V.: Dynamics of a prey-predator model: Untangling the role...
  • 43. DeAngelis, D.L., Goldstein, R.A., O’Neill, R.V.: A model for tropic interaction. Ecology 56(4), 881– 892 (1975)
  • 44. Tripathi, J.P., Bugalia, S., Jana, D., Gupta, N., Tiwari, V., Li, J., Sun, G.Q.: Modeling the cost of anti-predator strategy in a predator-prey...
  • 45. Cosner, C., DeAngelis, D.L., Ault, J.S., Olson, D.B.: Effects of spatial grouping on the functional response of predators. Theor. Popul....
  • 46. Tripathi, J.P., Abbas, S., Thakur, M.: Dynamical analysis of a prey-predator model with BeddingtonDeAngelis type function response incorporating...
  • 47. Tiwari, V., Tripathi, J.P., Jana, D., Tiwari, S.K., Upadhyay, R.K.: Exploring complex dynamics of spatial predator-prey system: role of...
  • 48. Pal, P.J., Mandal, G., Guin, L.N., Saha, T.: Allee effect and hunting-induced bifurcation inquisition and pattern formation in a modified...
  • 49. Naik, P.A., Ahmed, R., Faizan, A.: Theoretical and numerical bifurcation analysis of a discrete predatorprey system of Ricker type with...
  • 50. Abbasi, M.A., Samreen, M.: Analyzing multi-parameter bifurcation on a prey-predator model with the Allee effect and fear effect. Chaos...
  • 51. Mandal, G., Guin, L.N., Chakravarty, S., Han, R.: Dynamic complexities in a predator-prey model with prey refuge influenced by double...