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This study discusses the Leslie-Gower predator-prey model with the Sokol-Howell response function and anti-predator behavior. It is assumed that prey has anti-predator behavior that aims to reduce the risk of predation and not as an attempt by prey to find food. This study aims to formulate a Leslie-Gower predator-prey model with the Sokol-Howell response function and anti-predator behavior, analyze the model's equilibrium point and model interpretation. Stability analysis was carried out using the linearization method. The type of stability is determined based on the characteristic eigenvalues ​​obtained using Routh-Hurwitz criteria. The results of the analysis of the equilibrium point show that prey populations will exist and predators will become extinct if the anti-predator coefficient is greater than the intrinsic growth coefficient of predators, while prey and predator populations will always exist if the intrinsic growth coefficient of predators is greater than the anti-predator coefficient and fulfills other conditions required. Based on the numerical simulations performed, the interpretation is that an enlarged anti-predator coefficient increases the number of prey populations until they approach the carrying capacity, while predator populations decrease significantly and over time experience extinction.


predator-prey Leslie-Gower model, Sokol-Howell response function, anti predator

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  1. [1]M. L. Logan, S.G. Fernandez and R. Calsbeek, “Abiotic Constraints on The Activity of Tropical Lizards”, Functional Ecology, vol. 29, no.5, pp. 694-700. 2015.
  2. [2]S. N. Aftyah, “Analisis Dinamik Model predator-prey Leslie-ttower dengan Fungsi Respon Holling Tipe II’, Jurnal Ilmiah Teknologi dan Informasia ASIA (JITIKA), Vol. 9, No. 2. 2015.
  3. [3]S. J. Ali, N.Md. Arifin. N.Md, R.K. Naid, F. Ismail and N. Bachok, A three species of Leslie Gower predator-prey food chain model with Sokol Howell functional response. Institute for Mathematical Research, University Putra Malaysia. Malaysia, 2014.
  4. [4]P. H. Leslie,”Some Further Notes on the Use of Matrices in Population Mathematics”, Oxford University Press, Biometrika, vol. 35.1948.
  5. [5]S. G. Mortoja, P. Panja and S.K. Mondal, “Dynamics of a predator-prey Model with Stage Structure on Both Species and Anti-predator Behavior”, Informatics in Medicine Unlocked, vol. 10, pp. 50– 57. 2018.
  6. [6]S. Ruan and D. Xiao, “Global Anlysis in predator-prey System with Nonmotonic Functional Response”, Society for Industrial And Applied Mathematics, vol. 61, no.4, pp. 1445-1472. 2001.
  7. [7]S.H. Arsyad, Resmawan and N. Ahmad, “Analisis Model predator-prey Leslie-Gower dengan Pemberian Racun pada predator”, Jurnal Riset dan Aplikasi Matematika, vol.4, no.1, pp.1-16, 2020.
  8. [8]S. Saadah, Abadi and D. Savitri. “Model Interaksi Mangsa Pemangsa dengan Fungsi Respon Rasio Dependent Holling Tipe II dan Perilaku Anti Pemangsa”, Jurnal Ilmiah Matematika, vol.7, no.2, pp.6-9, 2019.
  9. [9]P. Panja, S.K. Mondal and Chattopadhyay, “Dynamical Effects of Anti-predator Behaviour of Adult prey in a predator-prey Model with Ratio-Dependent Functional Response”. Asian J. Journal of Mathematics and Physics, vol. 1, no. 1, pp. 19–32. 2017
  10. [10]H. S. Panigoro, “Analisis Dinamik Sistem predator-prey Model Leslie-Gower dengan Pemanenan Secara Konstan Terhadap predator”, Euler, vol.2, no. 1, pp. 1–12. 2014.
  11. [11]J. N. Ndam, J.P. Chollom and T.G. Kassem, T. G. “A Mathematical Model of Three-Species Interactions in an Aquatic Habitat”, ISRN Applied Mathematics, Pp. 1–11. 2012.
  12. [12]Z. Lie, W. Weiming, X.Yakui and J. Zhen, “Complex dynamics of a Holling-type IV predator prey model”, China: Department of Mathematics, North University of China. 2020.
  13. [13]A. Janssen, F. Faraji, T. Van der Hammen, S. Magalhães and M.W. Sabelis, “Interspecific Infanticide Deters predators” Ecology Letters, vol. 5. no. 4, pp. 490–494. 2002.
  14. [14]F. Verhulst, Nonlinear Differential Equations and Dynamical Systems, Springer – Verlag, New- York, USA, 1990.
  15. [15]L. Perko, Differential Equation and Dynamical System, New York, SpringerVerlag Berlin Heidelberg, 1991.
  16. [16]F. Gantmacher, The Theory of Matrices, Chelsea Publishing Company, 2020.