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Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA

Email: dr.volchenkov@gmail.com

Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania

Email: dumitru.baleanu@gmail.com


Dynamics of the Leslie Type Predator-Prey Model with Effect of Fear and Delay in the Prey Population

Discontinuity, Nonlinearity, and Complexity 12(2) (2023) 365--380 | DOI:10.5890/DNC.2023.06.010

D. Umapriya$^{1}$, V. Kalpana$^{1}$, M. A. Ramya$^{1}$, K. Karthiga$^{2}$

$^{1} $ Department of Mathematics, Dr. R. V. Arts and Science College, Coimbatore, Tamilnadu, India

$^{2}$ Department of Mathematics, M. Kumarasamy College of Engineering, Karur, Tamilnadu, India

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Abstract

References

  1. [1]  Lotka, A.J. (1925), Elements of physical biology, Williams and Wilkins.
  2. [2]  Beddington, J.R. (1975), Mutual interference between parasites or predators and its effect on searching efficiency, The Journal of Animal Ecology, 331-340.
  3. [3]  DeAngelis, D.L., Goldstein, R.A., and O'Neill, R.V. (1975), A model for tropic interaction, Ecology, 56(4), 881-892.
  4. [4]  Holling, C.S. (1959), The components of predation as revealed by a study of small mammal predation of the European pine sawfly, The Canadian Entomologist, 91(5), 293-320.
  5. [5]  Holling, C.S. (1959), Some characteristics of simple types of predation and parasitism, Canadian Entomologist, 91(7), 385-398.
  6. [6]  Liang, Z. and Honqwei, P. (2007), Qualitative analysis of a ratio-dependent Holling-Tanner model, Journal of Mathematical Analysis and Applications, 334(2), 954-964.
  7. [7]  Crowley, P.H. and Martin, E.K. (1989), Functional responses and interference within and between year classes of a dragonfly population, Journal of the North American Benthological Society, 8(3), 211-221.
  8. [8]  Fan, M. and Kuang, Y. (2004), Dynamics of a nonautonomous predator-prey system with the Beddington-DeAngelis functional response, Journal of Mathematical Analysis and Applications, 295(1), 15-39.
  9. [9]  Sivasamy, R., Vinoth, S., and Sathiyanathan, K. (2018), Exploring the dynamics of three species delayed food chain model with harvesting, Journal of Physics: Conference Series, 1139, 012028.
  10. [10]  Huang, T. (2004), Uniqueness of limit cycles of the predator-prey system with Beddington-DeAngelis functional response, Journal of Mathematical Analysis and Applications, 290(1), 113-112.
  11. [11]  Huang, T. (2003), Global analysis of the predator-prey system with Beddington-DeAngelis functional response, Journal of Mathematical Analysis and Applications, 281(1), 395-401.
  12. [12]  Cantrell, R.S. and Cosner, C. (2001), On the dynamics of predator-prey models with the Beddington-DeAngelis functional response, Journal of Mathematical Analysis and Applications, 257(1), 206-222.
  13. [13]  Sivasamy, R., Sivakumar, M., Sathiyanathan, K., and Balachandran, K. (2019), Dynamics of modified Leslie-Gower harvested predator-prey model with Bedddington-DeAngelis functional response, Discontinuity, Nonlinearity, and Complexity, 8(2), 111-125.
  14. [14]  Murray, J.D. (2003) Mathematical Biology I: An Introduction, volume I, Springer-Verlag.
  15. [15]  Hirsch, M.W., Smale, S., and Devaney, R.L. Differential Equations, Dynamical Systems, and an Introduction to Chaos, Academic press.
  16. [16]  Strogatz, S.H. (2018), Nonlinear Dynamics and Chaos: with Applications to Physics, Biology, Chemistry, and Engineering, CRC Press.
  17. [17]  Mondal, S., Maiti, A., and Samanta, G.P. (2018), Effects of fear and additional food in a delayed predator-prey model, Biophysical Reviews and Letters, 13(4), 157-177.
  18. [18]  Pal, S., Majhi, S., Mandal, S., and Pal, N. (2019), Role of fear in a predator-prey model with Beddington-DeAngelis functional response, Zeitschrift f{\"ur Naturforschung A}, 74(7), 581-595.
  19. [19]  Wang, X. and Zou, X. (2017), Modeling the fear effect in predator-prey interactions with adaptive avoidance of predators, Bulletin of mathematical biology, 79(6), 1325-1359.
  20. [20]  Wu, S. and Meng, X. (2021), Dynamics of a delayed predator-prey system with fear effect, herd behavior and disease in the susceptible prey, AIMS Mathematics, 6(4), 3654-3685.
  21. [21]  Sasmal, S. (2018), Population dynamics with multiple Allee effects induced by fear factors-A mathematical study on prey-predator interactions, Applied Mathematical Modelling, 64, 1-14.
  22. [22]  Liu, S., Beretta, E., and Breda, D. (2010), Predator-prey model of Beddington-DeAngelis type with maturation and gestation delays, Nonlinear Analysis: Real World Applications, 11(5), 4072-4091.
  23. [23]  Agrawal, R., Jana, D., Upadhyay, R., and Rao, V.S.H. (2017), Complex dynamics of sexually reproductive generalist predator and gestation delay in a food chain model: double Hopf-bifurcation to chaos, Nonlinear Analysis: Real World Applications, 55(1-2), 513-547.
  24. [24]  Jatav, K.S. and Dhar, J. (2015), Global behavior and Hopf bifurcation of a stage-structured prey-predator model with maturation delay for prey and gestation delay for predator, Journal of Biological Systems, 23(1), 57-77.
  25. [25]  Yang, R., Ren, H., and Cheng, X. (2017), A diffusive predator-prey system with prey refuge and gestation delay, Advances in Difference Equations, 2017(1), 158.
  26. [26]  Vinoth, S., Sivasamy, R., Sathiyanathan, K., Rajchakit, G., Hammachukiattikul, P., Vadivel, R., and Gunasekaran, N. (2021), Dynamical analysis of a delayed food chain model with additive Allee effect, Advances in Difference Equations, 2021, 54.
  27. [27]  Leslie, P.H. and Gower, J.C. (1960), The properties of a stochastic model for the predator-prey type of interaction between two species, Biometrika, 47(3/4), 219-234.
  28. [28]  Vinoth, S., Sivasamy, R., and Sathiyanathan, K. (2020), Qualitative analysis of a modified Leslie-Gower model with addictive allee effect and gestation delay, Discontinuity, Nonlinearity, and Complexity, 9(3), 461-476.
  29. [29]  Shengbin, Y. (2014), Global stability of a modified Leslie-Gower model with Beddington-DeAngelis functional response, Advances in Difference Equations, 2014, 84.
  30. [30]  Kuang, Y. (1990), Global stability of Gause-type predator-prey systems, Journal of Mathematical Biology, 28(4), 463-474.
  31. [31]  Aziz-Alaoui, M. and Okiye, M.D. (2003), Boundedness and global stability for a predator-prey model with modified Leslie-Gower and Holling-type II schemes, Applied Mathematics Letters, 16(7), 1069-1075.
  32. [32]  Chen, S. and Wei, J. (2012), Global stability and Hopf bifurcation in a delayed diffusive Leslie-Gower predator-prey system, International Journal of Bifurcation and Chaos, 22(03), 1250061.
  33. [33]  Harrison, G.W. (1979) Global stability of predator-prey interactions, Journal of Mathematical Biology, 8(2), 159-171.