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All issues Volume 21 (2026) Math. Model. Nat. Phenom., 21 (2026) 9 References
Open Access
Issue
Math. Model. Nat. Phenom.
Volume 21, 2026
Article Number 9
Number of page(s) 31
Section Population dynamics and epidemiology
DOI https://doi.org/10.1051/mmnp/2026006
Published online 23 March 2026
  1. C.S. Holling, The functional response of predators to prey density and its role in mimicry and population regulation. Mem. Entomol. Soc. Can. 97 (1965) 5–60. [Google Scholar]
  2. A. Oaten and W.W. Murdoch, Functional response and stability in predator-prey systems. Am. Nat. 109 (1975) 289–298. [Google Scholar]
  3. L.A. Real, The kinetics of functional response. Am. Nat. 111 (1977) 289–300. [Google Scholar]
  4. G.T. Skalski and J.F. Gilliam, Functional responses with predator interference: viable alternatives to the Holling type II model. Ecol. 82 (2001) 3083–3092. [Google Scholar]
  5. R. Arditi and L.R. Ginzburg, Coupling in predator-prey dynamics: ratio-dependence. J. Theor. Biol. 139 (1989) 311–326. [CrossRef] [Google Scholar]
  6. L. Cai, J. Yu and G. Zhu, A stage-structured predator-prey model with Beddington-DeAngelis functional response. J. Appl. Math. Comput. 26 (2008) 85–103. [Google Scholar]
  7. R.S. Cantrell and C. Cosner, On the dynamics of predator-prey models with the Beddington-Deangelis functional response, J. Math. Anal. Appl. 257 (2001) 206–222. [Google Scholar]
  8. J.P. Tripathi, S. Abbas and M. Thakur, Dynamical analysis of a prey-predator model with Beddington-DeAngelis type function response incorporating a prey refuge. Nonlinear Dyn. 80 (2015) 177–196. [Google Scholar]
  9. S. Bentout, S. Djilali and A. Atangana, Bifurcation analysis of an age-structured prey-predator model with infection developed in prey. Math. Methods Appl. Sci. 45 (2022) 1189–1208. [Google Scholar]
  10. K. Cao, Y. Li and Z. Liu, Sustained oscillations in an age-structured predator-prey model incorporating time delay. Nonlinear Anal. Real World Appl. 84 (2025) 104303. [Google Scholar]
  11. S. Wu, Z. Wang and S. Ruan, Hopf bifurcation in an age-structured predator-prey system with Beddington-Deangelis functional response and constant harvesting, J. Math. Biol. 88 (2024) 74. [Google Scholar]
  12. D. Yan, Y. Cao and Y. Yuan, Stability and Hopf bifurcation analysis of a delayed predator-prey model with age-structure and Holling III functional response. Z. Angew. Math. Phys. 74 (2023) 148. [Google Scholar]
  13. Y. Yuan and X. Fu, Asymptotic analysis for an age-structured predator-prey model with Beddington-DeAngelis functional response. Nonlinear Anal. Real World Appl. 85 (2025) 104345. [Google Scholar]
  14. J.M. Cushing, Integrodifferential Equations and Delay Models in Population Dynamics. Springer Science Business Media (2013). [Google Scholar]
  15. Y. Kuang et al., Delay Differential Equations: with Applications in Population Dynamics, Vol. 191. Academic Press (1993). [Google Scholar]
  16. S. Ruan, Absolute stability, conditional stability and bifurcation in Kolmogorov-type predator-prey systems with discrete delays. Q. Appl. Math. 59 (2001) 159–173. [Google Scholar]
  17. S. Zhao, K. Wang, M.K.C. Chong et al., The non-pharmaceutical interventions may affect the advantage in transmission of mutated variants during epidemics: a conceptual model for COVID-19. J. Theor. Biol. 542 (2022) 111105. [Google Scholar]
  18. T.K. Kar, Stability analysis of a prey-predator model incorporating a prey refuge. Commun. Nonlinear Sci. Numer. Simul. 10 (2005) 681–691. [Google Scholar]
  19. D. Xiao and S. Ruan, Bogdanov-Takens bifurcations in predator-prey systems with constant rate harvesting. Fields Inst. Commun. 21 (1999) 493–506. [Google Scholar]
  20. A. Martin and S. Ruan, Predator-prey models with delay and prey harvesting. J. Math. Biol. 43 (2001) 247–267. [Google Scholar]
  21. Z. Liu, P. Magal and S. Ruan, Hopf bifurcation for non-densely defined Cauchy problems. Z. Angew. Math. Phys. 62 (2011) 191–222. [Google Scholar]
  22. H.R. Thieme, Semiflows generated by Lipschitz perturbations of non-densely defined operators. Differential Integral Equations 3 (1990) 1035–1066. [Google Scholar]
  23. P. Magal and S. Ruan, Theory and Applications of Abstract Semilinear Cauchy Problems. Springer, New York (2018). [Google Scholar]
  24. P. Magal and S. Ruan, Semilinear Cauchy Problems with Non-dense Domain, Theory and Applications of Abstract Semilinear Cauchy Problems. Springer International Publishing, Cham (2018) 217–248. [Google Scholar]
  25. A. Ducrot, Z. Liu and P. Magal, Essential growth rate for bounded linear perturbation of non-densely defined Cauchy problems. J. Math. Anal. Appl. 341 (2008) 501–518. [Google Scholar]
  26. J. Hale, Theory of Functional Differential Equations. Springer-Verlag (1977). [Google Scholar]
  27. J.M. Jeschke, M. Kopp and R. Tollrian, Predator functional responses: discriminating between handling and digesting prey. Ecol. Monogr. 72 (2002) 95–112. [Google Scholar]
  28. S. Ruan and J. Wei, On the zeros of transcendental functions with applications to stability of delay differential equations with two delays. Dyn. Cont. Discr. Impuls. Syst. Ser. A Math. Anal. 10 (2003) 863–874. [Google Scholar]
  29. M. Iannelli, Mathematical Theory of Age-structured Population Dynamics. Giardini Editori E Stampatori, Pisa (1995). [Google Scholar]
  30. F. Sanchez, J.G. Calvo, E. Segura and Z. Feng, A partial differential equation model with age-structure and nonlinear recidivism: Conditions for a backward bifurcation and a general numerical implementation. Comput. Math. Appl. 78 (2019) 3916–3930. [Google Scholar]

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