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 predatorprey 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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