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All issues Volume 18 (2023) Math. Model. Nat. Phenom., 18 (2023) 13 References
Open Access
Issue
Math. Model. Nat. Phenom.
Volume 18, 2023
Article Number 13
Number of page(s) 24
Section Population dynamics and epidemiology
DOI https://doi.org/10.1051/mmnp/2023010
Published online 28 April 2023
  1. W. Abid, R. Yafia, M. Aziz-Alaoui and A. Aghriche, Turing instability and Hopf bifurcation in a modified Leslie-Gower predator-prey model with cross-diffusion. Int. J. Bifurc. Chaos 28 (2018) 1850089. [CrossRef] [Google Scholar]
  2. M.T. Alves and F.M. Hilker, Hunting cooperation and Allee effects in predators. J. Theor. Biol. 419 (2017) 13–22. [CrossRef] [Google Scholar]
  3. L. Berec, Impacts of foraging facilitation among predators on predator-prey dynamics. Bull. Math. Biol. 72 (2010) 94–121. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  4. C. Boesch, Cooperative hunting in wild chimpanzees. Animal Behav. 48 (1994) 653–667. [CrossRef] [Google Scholar]
  5. B.I. Camara and M. Aziz-Alaoui, Dynamics of a predator-prey model with diffusion. Dyn. Continu. Discr. Impulsive Syst. Ser. A 15 (2008) 897–906. [Google Scholar]
  6. B.I. Camara and M. Aziz-Alaoui, Turing and Hopf patterns formation in a predator-prey model with Leslie-Gower-type functional response. Dyn. Continu. Discr. Impulsive Syst. Ser. B 16 (2009) 479–488. [Google Scholar]
  7. F. Capone, M.F. Carfora, R. De Luca and I. Torcicollo, Turing patterns in a reaction-diffusion system modeling hunting cooperation. Math. Comput. Simul. 165 (2019) 172–180. [CrossRef] [Google Scholar]
  8. Y. Chow, S.R.-J. Jang and H.-M. Wang, Cooperative hunting in a discrete predator-prey system II. J. Biolog. Dyn. 13 (2019) 247–264. [CrossRef] [PubMed] [Google Scholar]
  9. S. Creel and D. Christianson, Relationships between direct predation and risk effects. Trends Ecol. Evol. 23 (2008) 194–201. [CrossRef] [Google Scholar]
  10. S. Creel, D. Christianson, S. Liley and J.A. Winnie Jr, Predation risk affects reproductive physiology and demography of elk. Science 315 (2007) 960–960. [CrossRef] [PubMed] [Google Scholar]
  11. W. Cresswell, Predation in bird populations. J. Ornithol. 152 (2011) 251–263. [CrossRef] [Google Scholar]
  12. D.P. Hector, Cooperative hunting and its relationship to foraging success and prey size in an avian predator. Ethology 73 (1986) 247–257. [Google Scholar]
  13. S.R.-J. Jang, W. Zhang and V. Larriva, Cooperative hunting in a predator-prey system with Allee effects in the prey. Nat. Resource Model. 31 (2018) e12194. [CrossRef] [Google Scholar]
  14. W.-T. Li and S.-L. Wu, Traveling waves in a diffusive predator-prey model with Holling type-III functional response. Chaos Solitons Fract. 37 (2008) 476–486. [CrossRef] [Google Scholar]
  15. Y. Lou and W.-M. Ni, Diffusion, self-diffusion and cross-diffusion, J. Differ. Equ. 131 (1996) 79–131. [CrossRef] [Google Scholar]
  16. D.W. Macdonald, The ecology of carnivore social behaviour. Nature 301 (1983) 379–384. [CrossRef] [Google Scholar]
  17. N. Mukherjee and M. Banerjee, Hunting cooperation among slowly diffusing specialist predators can induce stationary Turing patterns. Physica A 599 (2022) 127417. [CrossRef] [Google Scholar]
  18. J.D. Murray, Discussion: Turing’s theory of morphogenesis—its influence on modelling biological pattern and form. Bull. Math. Biol. 52 (1990) 117–152. [CrossRef] [Google Scholar]
  19. J.D. Murray, Vol. 3 of Mathematical biology II: spatial models and biomedical applications. Springer New York (2001). [Google Scholar]
  20. A. Narcisa and D. Gabriel, On a prey—predator reaction—diffusion system with Holling type III functional response. J. Comput. Appl. Math. 235 (2010). [MathSciNet] [Google Scholar]
  21. D.G. Orlovskij, The Fredholm solvability of inverse problems for abstract differential equations., in Ill-posed problems in natural sciences. Proceedings of the international conference held in Moscow (Russia), August 19-25, 1991. Utrecht: VSP; Moscow: TVP Science Publishers (1992), pp. 367–374. [Google Scholar]
  22. Q. Ouyang, Pattern Formation in Reaction-Diffusion Systems. Shanghai Sci. & Edu. Press, Shanghai (2000). [Google Scholar]
  23. Q. Ouyang, Nonlinear science and the pattern dynamics introduction. Peking University Press, Beijing (2010). [Google Scholar]
  24. C. Packer, D. Scheel and A.E. Pusey, Why lions form groups: food is not enough. Am. Natural. 136 (1990) 1–19. [CrossRef] [Google Scholar]
  25. S. Pal, N. Pal and J. Chattopadhyay, Hunting cooperation in a discrete-time predator-prey system. Int. J. Bifurc. Chaos 28 (2018) 1850083. [CrossRef] [Google Scholar]
  26. U.D. Sheng Chen and U.C. Tauber, Evolutionary dynamics and competition stabilize three-species predator—prey communities. Ecol. Complex. 36 (2018) 57–72. [CrossRef] [Google Scholar]
  27. T.Z. Shengqiang Zhang and S. Yuan, Dynamics of a stochastic predator-prey model with habitat complexity and prey aggregation. Ecol. Complex. 45 (2021) 100889. [CrossRef] [Google Scholar]
  28. T. Singh and S. Banerjee, Spatial aspect of hunting cooperation in predators with Holling type II functional response. J. Biol. Syst. 26 (2018) 511–531. [CrossRef] [Google Scholar]
  29. T. Singh, R. Dubey and V.N. Mishra, Spatial dynamics of predator-prey system with hunting cooperation in predators and type I functional response. AIMS Math. 5 (2019) 673–684. [Google Scholar]
  30. A. Turing, Philosophical the royal biological transqfctions society sciences. Phil. Trans. R. Soc. Lond. B 237 (1952) 37–72. [CrossRef] [Google Scholar]
  31. G.W. Uetz, Foraging strategies of spiders. Trends Ecol. Evol. 7 (1992) 155–159. [CrossRef] [Google Scholar]
  32. E. Venturino and S. Petrovskii, Spatiotemporal behavior of a prey-predator system with a group defense for prey. Ecol. Complex. 14 (2013) 37–47. [CrossRef] [Google Scholar]
  33. D. Wu and M. Zhao, Qualitative analysis for a diffusive predator-prey model with hunting cooperative. Physica A 515 (2019) 299–309. [CrossRef] [MathSciNet] [Google Scholar]
  34. R. Yadav, N. Mukherjee and M. Sen, Spatiotemporal dynamics of a prey-predator model with Allee effect in prey and hunting cooperation in a Holling type III functional response. Nonlinear Dyn. 107 (2022) 1397–1410. [CrossRef] [Google Scholar]
  35. E.P. Zemskov, V.K. Vanag and I.R. Epstein, Amplitude equations for reaction-diffusion systems with cross diffusion. Phys. Rev. E 84 (2011) 036216. [CrossRef] [PubMed] [Google Scholar]

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