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All issues Volume 20 (2025) Math. Model. Nat. Phenom., 20 (2025) 26 References
Open Access
Issue
Math. Model. Nat. Phenom.
Volume 20, 2025
Article Number 26
Number of page(s) 32
Section Population dynamics and epidemiology
DOI https://doi.org/10.1051/mmnp/2025019
Published online 17 October 2025
  1. P.F. Verhulst, Notice sur la loi que la population suit dans son accroissement. Correspondence Math. Phys. 10 (1838) 113–121. [Google Scholar]
  2. J. Arino, L. Wang and G.S.K. Wolkowicz, An alternative formulation for a delayed logistic equation. J. Theor. Biol. 241 (2006) 109–119. [Google Scholar]
  3. S. Kingsland, The refractory model: the logistic curve and the history of population ecology. Q. Rev. Biol. 57 (1982) 29–52. [Google Scholar]
  4. G.E. Hutchinson, Circular causal systems in ecology. Ann. NY Acad. Sci. 50 (1948) 221–246. [Google Scholar]
  5. E.M. Wright, A non-linear difference-differential equation. J. Reine Angew. Math. 494 (1955) 66–87. [Google Scholar]
  6. B. Bánhelyi, T. Csendes, T. Krisztin and A. Neumaier, Global attractivity of the zero solution for Wright’s equation. SIAM J. Appl. Dyn. Syst. 13 (2014) 537–563. [Google Scholar]
  7. S. Ruan, Delay differential equations in single species dynamics, in Delay Differential Equations and Applications, edited by O. Arino, E. Ait Dads, and M. Hbid. Springer, Dordrecht (2006) 477-517. [Google Scholar]
  8. J.B. van den Berg and J. Jaquette, A proof of Wright’s conjecture. J. Differ. Equ. 264 (2018) 7412–7462. [Google Scholar]
  9. C.J. Lin, L. Wang and G.S.K. Wolkowicz, An alternative formulation for a distributed delayed logistic equation. Bull. Math. Biol. 80 (2018) 1713–1735. [Google Scholar]
  10. C.J. Lin, T.-H. Hsu and G.S.K. Wolkowicz, Population growth and competition models with decay and competition consistent delay. J. Math. Biol. 84 (2022) 39. [Google Scholar]
  11. R.E. Baker and G. Röst, Global dynamics of a novel delayed logistic equation arising from cell biology. J. Nonlinear Sci. 30 (2020) 397–418. [Google Scholar]
  12. R. Moreno-Opo, A. Trujillano and A. Margalida, Larger size and older age confer competitive advantage: dominance hierarchy within European vulture guild. Sci. Rep. 10 (2020) 2430. [Google Scholar]
  13. D. Sol, D.M. Santos and J. Garcia, Competition for food in urban pigeons: the cost of being juvenile. Condor 100 (1998) 298–304. [Google Scholar]
  14. I.M. Bomze, Lotka–Volterra equation and replicator dynamics: a two-dimensional classification. Biol. Cybernet. 48 (1983) 201–211. [Google Scholar]
  15. Z. Hou, Permanence and extinction in competitive Lotka–-Volterra systems with delays. Nonlinear Anal. RWA 12 (2011) 2130–2141. [Google Scholar]
  16. M. Saeedian, E. Pigani, A. Maritan, S. Suweis and S. Azaele, Effect of delay on the emergent stability patterns in generalized Lotka-–Volterra ecological dynamics. Phil. Trans. R. Soc. A 380 (2022) 20210245. [Google Scholar]
  17. S. Ahmad, On the nonautonomous Volterra–Lotka competition equations. Am. Math. Soc. 117 (1993) 199–205. [Google Scholar]
  18. J. Zhao and J. Jiang, Average conditions for permanence and extinction in nonautonomous Lotka-–Volterra system. J. Math. Anal. Appl. 229 (2004) 663–675. [Google Scholar]
  19. Z. Li, B. Dai and Y. Chen, Coexistence and competitive exclusion in a time-periodic Lotka–Volterra competitiondiffusion system. J. Differ. Equ. 374 (2023) 654–698. [Google Scholar]
  20. C.-Y. Cheng, K.-H. Lin and C.-W. Shih, Intra- and inter-specific competitions of two stage-structured species in a patchy environment. J. Dyn. Differ. Equ. 36 (2024) 2879–2924. [Google Scholar]
  21. M. El-Hachem and N.J. Beeton, Coexistence in two-species competition with delayed maturation. J. Math. Biol. 88 (2024) 11. [Google Scholar]
  22. J.K. Hale and S.M. Verduyn Lunel, Introduction to Functional-Differential Equations. Applied Mathematical Sciences, Vol. 99. Springer, New York (1993). [Google Scholar]
  23. N.D. Hayes, Roots of the transcendental equation associated with a certain difference-differential equation. J. Lond. Math. Soc. 25 (1950) 226–232. [Google Scholar]
  24. W.M. Hirsch, H. Hanisch and J.P. Gabriel, Differential equation models of some parasitic infections: methods for the study of asymptotic behavior. Commun. Pur. Appl. Math. 38 (1985) 733–753. [Google Scholar]
  25. H.R. Thieme, Persistence under relaxed point-dissipativity (with application to an endemic model). SIAM J. Math. Anal. 24 (1993) 407–435. [Google Scholar]
  26. E. Beretta and Y. Kuang, Geometric stability switch criteria in delay differential systems with delay dependent parameters. J. Math. Anal. 33 (2002) 1144–1165. [Google Scholar]
  27. H.L. Smith, Monotone dynamical systems: an introduction to the theory of competitive and cooperative systems, in Mathematical Surveys and Monographs Vol. 41. AMS, Providence, RI (1995). [Google Scholar]
  28. X.-Q. Zhao, Basic reproduction ratios for periodic compartmental models with time delay. J. Dyn. Differ. Equ. 29 (2017) 67–82. [Google Scholar]
  29. X. Wang and X.-Q. Zhao, Dynamics of a time-delayed Lyme disease model with seasonality. SIAM J. Appl. Dyn. Syst. 16 (2017) 853–881. [Google Scholar]
  30. X. Liang, L. Zhang and X.-Q. Zhao, Basic reproduction ratios for periodic abstract functional differential equations (with application to a spatial model for Lyme disease). J. Dyn. Differ. Equ. 31 (2019) 1247–1278. [Google Scholar]

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