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Research Article

Complex dynamics of a predator–prey model with opportunistic predator and weak Allee effect in prey

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Article: 2225545 | Received 22 Aug 2022, Accepted 10 Jun 2023, Published online: 20 Jun 2023

References

  • A.S. Ackleh, M.I. Hossain, A. Veprauskas, and A. Zhang, Persistence and stability analysis of discrete-time predator–prey models: A study of population and evolutionary dynamics, J. Difference Equ. Appl. 25 (2019), pp. 1568–1603.
  • C. Arancibia-Ibarra and J. Flores, Modelling and analysis of a modified May–Holling–Tanner predator–prey model with Allee effect in the prey and an alternative food source for the predator, Math. Biosci. Eng. 17 (2020), pp. 8052–8073.
  • C. Arancibia-Ibarra and J. Flores, Dynamics of a Leslie–Gower predator–prey model with Holling type II functional response, Allee effect and a generalist predator, Math. Comput. Simulation 188 (2021), pp. 1–22.
  • C. Arancibia-Ibarra, M. Bode, J. Flores, G. Pettet, and P. Van Heijster, Turing patterns in a diffusive Holling–Tanner predator–prey model with an alternative food source for the predator, Commun. Nonlinear Sci. Numer. Simul. 99 (2021), Article ID 105802.
  • D. Bai, Y. Kang, S. Ruan, and L. Wang, Dynamics of an intraguild predation food web model with strong Allee effect in the basal prey, Nonlinear Anal. Real World Appl. 58 (2021), Article ID 103206, 36 pp.
  • A.A. Berryman and P. Kindlmann, Population Systems. A General Introduction, Springer, 2008.
  • S. Biswas, S.K. Sasmal, S. Samanta, Md. Saifuddin, N. Pal, and J. Chattopadhyay, Optimal harvesting and complex dynamics in a delayed eco-epidemiological model with weak Allee effects, Nonlinear Dynam. 87 (2017), pp. 1553–1573.
  • L.S. Chen, Mathematical Ecology Model and Research Method, Science Press, Beijing, 2017.
  • Y.-S. Chen, T. Giletti, and J.-S. Guo, Persistence of preys in a diffusive three species predator–prey system with a pair of strong-weak competing preys, J. Differ. Equ. 281 (2021), pp. 341–378.
  • S.-N. Chow, C.Z. Li, and D. Wang, Normal Forms and Bifurcation of Planar Vector Fields, Cambridge University Press, Cambridge, 1994.
  • F. Courchamp, T. Clutton-Brock, and B. Grenfell, Inverse dependence and the Allee effect, Trends Ecol. Evol. 14 (1999), pp. 405–410.
  • Y. Dai, Y. Zhao, and B. Sang, Four limit cycles in a predator–prey system of Leslie type with generalized Holling type III functional response, Nonlinear Anal. Real World Appl. 50 (2019), pp. 218–239.
  • B. Dennis, Allee effects: Population growth, critical density, and the chance of extinction, Nat. Resour. Model. 3 (1989), pp. 481–538.
  • E. González-Olivares and A. Rojas-Palma, Global stability in a modified Leslie-Gower type predation model assuming mutual interference among generalist predators, Math. Biosci. Eng. 17 (2020), pp. 7708–7731.
  • E. González-Olivares, C. Arancibia-Ibarra, A. Rojas-Palma, and B. González-Yañez, Bifurcations and multistability on the May-Holling-Tanner predation model considering alternative food for the predators, Math. Biosci. Eng. 16 (2019), pp. 4274–4298.
  • E. González-Olivares, C. Arancibia-Ibarra, A. Rojas-Palma, and B. González-Yañez, Dynamics of a modified Leslie-Gower predation model considering a generalist predator and the hyperbolic functional response, Math. Biosci. Eng. 16 (2019), pp. 7995–8024.
  • J. Jiao, W. Zhang, and P. Yu, Tristable phenomenon in a predator–prey system arising from multiple limit cycles bifurcation, Internat. J. Bifur. Chaos Appl. Sci. Eng. 30 (2020), Article ID 2050129, 23 pp.
  • Yu.A. Kuznetsov, Elements of Applied Bifurcation Theory, 3rd ed., Applied Mathematical Sciences Vol. 112, Springer-Verlag, New York, USA, 2004.
  • L. Meng, C. Du, and M. Deng, Persistence and extinction of a modified Leslie–Gower Holling-type II stochastic predator–prey model with impulsive toxicant input in polluted environments, Nonlinear Anal. Hybrid Syst. 27 (2018), pp. 177–190.
  • H. Merdan, Stability analysis of a Lotka–Volterra type predator–prey system involving Allee effects, ANZIAM J. 52 (2010), pp. 139–145.
  • L. Perko, Differential Equations and Dynamical Systems, 3rd ed., Springer-Verlag, New York, 2001.
  • G. Ren and B. Liu, Global existence and convergence to steady states for a predator–prey model with both predator–and prey–taxis, Discrete Contin. Dyn. Syst. 42 (2022), pp. 759–779.
  • D. Sen, S. Petrovskii, S. Ghorai, and M. Banerjee, Rich bifurcation structure of prey-predator model induced by the Allee effect in the growth of generalist predator, Internat. J. Bifur. Chaos Appl. Sci. Eng. 30 (2020), Article ID 2050084, 22 pp.
  • D. Sen, S. Ghorai, S. Sharma, and M. Banerjee, Allee effect in prey's growth reduces the dynamical complexity in prey-predator model with generalist predator, Appl. Math. Model. 91 (2021), pp. 768–790.
  • G. Seo and G.S.K. Wolkowicz, Pest control by generalist parasitoids: A bifurcation theory approach, Discrete Contin. Dyn. Syst. Ser. S 13 (2020), pp. 3157–3187.
  • Y. Tian and M. Han, Hopf and homoclinic bifurcations for near-Hamiltonian systems, J. Differ. Equ.262 (2017), pp. 3214–3234.
  • J.P. Tripathi, P.S. Mandal, and A. Poonia, A widespread interaction between generalist and specialist enemies: The role of intraguild predation and Allee effect, Appl. Math. Model. 89 (2021), pp. 105–135.
  • K. Vishwakarma and M. Sen, Role of Allee effect in prey and hunting cooperation in a generalist predator, Math. Comput. Simulation 190 (2021), pp. 622–640.
  • W. Wang, Y.-n. Zhu, Y. Cai, and W. Wang, Dynamical complexity induced by Allee effect in a predator–prey model, Nonlinear Anal. Real World Appl. 16 (2014), pp. 103–119.
  • C. Zhang, Pattern formation with jump discontinuity in a macroalgae-herbivore model with strong Allee effect in macroalgae, J. Math. Anal. Appl. 504 (2021), Article ID 125371, 26 pp.
  • Z.F. Zhang, T.R. Ding, W.Z. Huang, and Z.X. Dong, Qualitative Theory of Differential Equations, American Mathematical Society, Providence, 1992.
  • Z. Zhu, Y. Chen, Z. Li, and F. Chen, Stability and bifurcation in a Leslie-Gower predator–prey model with Allee effect, Internat. J. Bifur. Chaos Appl. Sci. Eng. 32 (2022), Article ID 2250040, 25 pp.