Implementation of non-standard finite difference on a predator prey model considering cannibalism on predator and harvesting on prey
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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. DOI:10.1016/j.mbs.2018.11.004
J. Li et al., “Impact of cannibalism on dynamics of a structured predator–prey system,” Applied Mathematical Modelling, vol. 78, pp. 1–19, 2020. DOI:10.1016/j.apm.2019.09.022
M. S. Islam and M. S. Rahman, “Dynamics of cannibalism in the predator in a prey refuge functional response dependent predator-prey model,” IJEES, vol. 45, 2024.
Z. Hammouch et al., “Dynamics investigation and numerical simulation of fractional-order predator-prey model with holling type II functional response,” Discrete and Continuous Dynamical Systems-S, vol. 18, no. 5, pp. 1230–1266, 2025. DOI:10.3934/dcdss.2024181
P. Sireeshadevi and G. R. Kumar, “Dynamical behavior of an eco-epidemiological model incorporating holling type-II functional response with prey refuge and constant prey harvesting,” Network Biology, vol. 14, no. 3, pp. 228–241, 2024.
Ö. A. Gümüs¸, “Dynamics of a prey-predator system with harvesting effect on prey,” Chaos Theory and Applications, vol. 4, no. 3, pp. 144–151, 2022. DOI:10.51537/chaos.1183113
N. Imamah Ah et al., “The Dynamics of a Predator-Prey Model Involving Disease Spread In Prey and Predator Cannibalism,” Jambura Journal of Biomathematics (JJBM), vol. 4, no. 2, pp. 119–125, 2023. DOI:10.37905/jjbm.v4i2.21495
L. K. Beay et al., “A Stage-structure Leslie-Gower Model with Linear Harvesting and Disease in Predator,” Jambura Journal of Biomathematics, vol. 4, no. 2, pp. 155–163, 2023. DOI:10.37905/jjbm.v4i2.22047
A. Lahay et al., “Dynamics of a predator-prey model incorporating infectious disease and quarantine on prey,” Jambura Journal of Mathematics, vol. 3, no. 2, pp. 75–81, 2022. DOI:10.37905/jjbm.v4i2.22047
A. Sirén and K. Parvinen, “A spatial bioeconomic model of the harvest of wild plants and animals,” Ecological Economics, vol. 116, pp. 201–210, 2015. DOI:10.1016/j.ecolecon.2015.04.015
Rashi et al., “Cooperation and harvesting-induced delays in a predator–prey model with prey fear response: A crossing curves approach,“ Chaos, Solitons & Fractals, vol. 194, p. 116132, 2025. DOI:10.1016/j.chaos.2025.116132
B. E. Kashem and H. F. Al-Husseiny, “The dynamic of two prey–one predator food web model with fear and harvesting,“ Partial Differential Equations in Applied Mathematics, vol. 11, p. 100875, 2024. DOI:10.1016/j.padiff.2024.100875
S. Roy and P. K. Tiwari, “Bistability in a predator–prey model characterized by the crowley–martin functional response: Effects of fear, hunting cooperation, additional foods and nonlinear harvesting,“ Mathematics and Computers in Simulation, vol. 228, pp. 274–297, 2025. DOI:10.1016/j.matcom.2024.09.001
N. Ahmed et al., “Pattern formation and analysis of reaction–diffusion ratio-dependent prey–predator model with harvesting in predator,“ Chaos, Solitons & Fractals, vol. 251, p. 115164, 2024. DOI:10.1016/j.chaos.2024.115164
N. Sarif et al., “Spatio-temporal dynamics in a delayed prey–predator model with nonlinear prey refuge and harvesting,“ Chaos, Solitons & Fractals, vol. 186, p. 115247, 2024. DOI:10.1016/j.chaos.2024.115247
Y. Gao, M. Banerjee, and T. V. Ta, “Dynamics of infectious diseases in predator–prey populations: A stochastic model, sustainability, and invariant measure,“ Mathematics and Computers in Simulation, vol. 227, pp. 103–120, 2025. DOI:10.1016/j.matcom.2024.07.031
M. Wang and S. Yao, “The dynamics of an eco-epidemiological prey–predator model with infectious diseases in prey,“ Communications in Nonlinear Science and Numerical Simulation, vol. 132, p. 107902, 2024. DOI:10.1016/j.cnsns.2024.107902
A. Xiang and L. Wang, “Boundedness and stabilization in a predator-prey model with prey-taxis and disease in predator species,“ Journal of Mathematical Analysis and Applications, vol. 522, no. 1, p. 126953, 2023. DOI:10.1016/j.jmaa.2022.126953
Y. Cao et al., “Investigating the spread of a disease on the prey and predator interactions through a nonsingular fractional model,“ Results in Physics, vol. 32, p. 105084, 2022. DOI:10.1016/j.rinp.2021.105084
N. Li and M. Yan, “Bifurcation control of a delayed fractional-order prey-predator model with cannibalism and disease,“ Physica A: Statistical Mechanics and its Applications, vol. 600, p. 127600, 2022. DOI:10.1016/j.physa.2022.127600
S. G. Mortoja, P. Panja, and S. K. Mondal, “Dynamics of a predator-prey model with nonlinear incidence rate, Crowley-martin type functional response and disease in prey population,“ Ecological Genetics and Genomics, vol. 10, p. 100035, 2019. DOI:10.1016/j.egg.2018.100035
W. Mbava, J. Mugisha, and J. Gonsalves, “Prey, predator and super-predator model with disease in the super-predator,“ Applied Mathematics and Computation, vol. 297, pp. 92–114, 2017. DOI:10.1016/j.amc.2016.10.034
G. Barabás, M. J. Michalska-Smith, and S. Allesina, “Self-regulation and the stability of large ecological networks,” Nature ecology & evolution, vol. 1, no. 12, pp. 1870–1875, 2017.
H. Deng et al., “Dynamic behaviors of lotka–volterra predator–prey model incorporating predator cannibalism,” Advances in Difference Equations, vol. 2019, pp. 1–17, 2019. DOI:10.1186/s13662-019-2289-8
M. Rayungsari et al., “A nonstandard numerical scheme for a predator-prey model involving predator cannibalism and refuge,” Communication in Biomathematical Sciences, vol. 6, no. 1, pp. 11–23, 2023. DOI:10.5614/cbms.2023.6.1.2
R. E. Mickens, Nonstandard finite difference models of differential equations. world scientific, 1993. DOI:10.1142/2081
DOI: https://doi.org/10.37905/jjbm.v6i1.30550
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