Dynamics of a stage–structure Rosenzweig–MacArthur model with linear harvesting in prey and cannibalism in predator

Lazarus Kalvein Beay, Maryone Saija

Abstract


A kind of stage-structure Rosenzweig–MacArthur model with linear harvesting in prey and cannibalism in predator is investigated in this paper. By analyzing the model, local stability of all possible equilibrium points is discussed. Moreover, the model undergoes a Hopf–bifurcation around the interior equilibrium point. Numerical simulations are carried out to illustrate our main results.


Keywords


Stage-structure; Rosenzweig-MacArthur model; linear harvesting; cannibalism; stability; Hopf-bifurcation

Full Text:

PDF [ENGLISH]

References


A. S. Purnomo, I. Darti, and A. Suryanto, “Dynamics of eco-epidemiological model with harvesting,” AIP Conference Proceedings, vol. 1913, no. 020018, 2017.

H. S. Panigoro and E. Rahmi, “Global stability of a fractional-order logistic growth model with infectious disease,” Jambura Journal of Biomathematics, vol. 1, no. 2, pp. 49–56, 2020.

A. Suryanto, I. Darti, H. S. Panigoro, and A. Kilicman, “A fractional-order predator–prey model with ratio-dependent functional response and linear harvesting,” Mathematics, vol. 7, no. 11, p. 1100, 2019.

H. S. Panigoro, A. Suryanto, W. M. Kusumawinahyu, and I. Darti, “A Rosenzweig–MacArthur model with continuous threshold harvesting in predator involving fractional derivatives with power law and mittag–leffler kernel,” Axioms, vol. 9, no. 4, p. 122, 2020.

P. Santra, “Discrete-time prey-predator model with q-logistic growth for prey incorporating square root functional response,” Jambura Journal of Biomathematics, vol. 1, no. 2, pp. 41–48, 2020.

L. K. Beay, A. Suryanto, I. Darti, and Trisilowati, “Stability of a stage-structure Rosenzweig-MacArthur model incorporating Holling type-II functional response,” IOP Conference Series: Materials Science and Engineering, vol. 546, no. 5, 2019.

L. K. Beay and M. Saija, “A stage-structure Rosenzweig-MacArthur model with effect of prey refuge,” Jambura Journal of Biomathematics, vol. 1, no. 1, pp. 1–7, 2020.

L. Kalvein Beay, A. Suryanto, I. Darti, Trisilowati, L. K. Beay, A. Suryanto, I. Darti, and Trisilowati, “Hopf bifurcation and stability analysis of the Rosenzweig-MacArthur predator-prey model with stage structure in prey,” Mathematical Biosciences and Engineering, vol. 17, no. 4, pp. 4080–4097, 2020.

K. Chakraborty, M. Chakraborty, and T. K. Kar, “Optimal control of harvest and bifurcation of a prey-predator model with stage structure,” Applied Mathematics and Computation, vol. 217, no. 21, pp. 8778 8792, 2011.

K. Belkhodja, A. Moussaoui, and M. A. Alaoui, “Optimal harvesting and stability for a prey–predator model,” Nonlinear Analysis: Real World Applications, vol. 39, pp. 321–336, 2018.

Z. Gui and W. Ge, “The effect of harvesting on a predator-prey system with stage structure,” Ecological Modelling, vol. 187, no. 2-3, pp. 329–340, 2005.

S. Toaha and M. Abu Hassan, “Stability analysis of predator - prey population model with time delay and constant rate of harvesting,” Punjub University Journal of Mathematics, vol. 40, pp. 37–48, 2008.

S. Toaha, “The effect of harvesting with threshold on the dynamics of prey predator model,” Journal of Physics: Conference Series, vol. 1341, no. 6, p. 062021, 2019.

S. Maisaroh, R. Resmawan, and E. Rahmi, “Analisis kestabilan model predator-prey dengan infeksi penyakit pada prey dan pemanenan proporsional pada predator,” Jambura Journal of Biomathematics, vol. 1, no. 1, pp. 8–15, 2020.

Y. Lv, R. Yuan, and Y. Pei, “Dynamics in two nonsmooth predator-prey models with threshold harvesting,” Nonlinear Dynamics, vol. 74, no. 1-2, pp. 107–132, 2013.

X.-P. Yan and C.-H. Zhang, “Global stability of a delayed diffusive predator–prey model with prey harvesting of Michaelis–Menten type,” Applied Mathematics Letters, vol. 114, p. 106904, 2021.

T. K. Ang and H. M. Safuan, “Dynamical behaviors and optimal harvesting of an intraguild prey-predator fishery model with Michaelis-Menten type predator harvesting,” Biosystems, vol. 202, no. January, p. 104357, 2021.

X. Yu, Z. Zhu, L. Lai, and F. Chen, “Stability and bifurcation analysis in a single-species stage structure system with Michaelis–Menten-type harvesting,” Advances in Difference Equations, vol. 2020, no. 1, p. 238, 2020.

Q. Lin, C. Liu, X. Xie, and Y. Xue, “Global attractivity of Leslie–Gower predator-prey model incorporating prey cannibalism,” Advances in Difference Equations, vol. 2020, no. 1, 2020.

B. Buonomo and D. Lacitignola, “On the stabilizing effect of cannibalism in stage-structured population models,” Mathematical Biosciences and Engineering, vol. 3, no. 4, pp. 717–731, 2006.

F. Zhang, Y. Chen, and J. Li, “Dynamical analysis of a stage-structured predator-prey model with cannibalism,” Mathematical Biosciences, vol. 307, pp. 33–41, 2019.

H. Deng, F. Chen, Z. Zhu, and Z. Li, “Dynamic behaviors of Lotka–Volterra predator–prey model incorporating predator cannibalism,” Advances in Difference Equations, vol. 2019, no. 1, pp. 1–17, 2019.

Y. Kang, M. Rodriguez-Rodriguez, and S. Evilsizor, “Ecological and evolutionary dynamics of two-stage models of social insects with egg cannibalism,” Journal of Mathematical Analysis and Applications, vol. 430, no. 1, pp. 324–353, 2015.

M. Rodriguez-Rodriguez and Y. Kang, “Colony and evolutionary dynamics of a two-stage model with brood cannibalism and division of labor in social insects,” Natural Resource Modeling, vol. 29, no. 4, pp. 633–662, 2016.

Y. Cai, C. Zhao, W. Wang, and J. Wang, “Dynamics of a Leslie-Gower predator-prey model with additive Allee effect,” Applied Mathematical Modelling, vol. 39, no. 7, pp. 2092–2106, 2015.




DOI: https://doi.org/10.34312/jjbm.v2i1.10470

Copyright (c) 2021 Lazarus Kalvein Beay, Maryone Saija

Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

Jambura Journal of Biomathematics (JJBM) has been indexed by:

                          EDITORIAL OFFICE OF JAMBURA JOURNAL OF BIOMATHEMATICS

 Department of Mathematics, Faculty of Mathematics and Natural Science, Universitas Negeri Gorontalo
Jl. Prof. Dr. Ing. B. J. Habibie, Moutong, Tilongkabila, Kabupaten Bone Bolango 96554, Gorontalo, Indonesia
 Email: editorial.jjbm@ung.ac.id
 +6281356190818 (Call/SMS/WA)
 Jambura Journal of Biomathematics (JJBM) by Department of Mathematics Universitas Negeri Gorontalo is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.  Powered by Public Knowledge Project OJS.