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Hazel Mae R. Diza, Joel M. Addawe


In this study, we proposed to study the mathematical analysis of a Leslie Gower type predator prey model. The model considers the dynamics of a predator and prey populations with constant-effort harvesting applied in the predator population. We then computed and identified the existence of different equilibrium points of the model and investigated local stabilities of those points. We then proved that the system undergoes transcritical bifurcation. 


Predator-prey; constant-effort harvesting; equilibrium points

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Baca¨er, N. 2011. “A short history of mathematical population dynamics”, Springer Science & Business Media.

Beddington, J. Cooke, J. 1982. “Harvesting from a prey-predator complex”, Ecological Modelling143-4155–177.

Beddington, J. May, R. 1980. “Maximum sustainable yields in systems subject to harvesting at more than one trophic level”, Mathematical Biosciences513-4261–281.

Boyce, WE., DiPrima, RC. Haines, CW. 1969. “Elementary differential equations and boundary value problems”,(9). Wiley New York.

Clark, C. 1990. “Mathematical bioeconomics”.

Edelstein-Keshet, L. 1988. “Mathematical models in biology(46)”, Siam.

Gong, Yj. Huang, Jc. 2014. “Bogdanov-Takens bifurcation in a Leslie-Gower predator-prey model with prey harvesting”, Acta Mathematicae Applicatae Sinica, EnglishSeries301239–244.

Hsu, SB. Huang, TW. 1995. “Global stability for a class of predator-prey systems”, SIAM Journal on Applied Mathematics553763–783.

Hu, D. Cao, H. 2017. “Stability and bifurcation analysis in a predator–prey system with Michaelis–Menten type predator harvesting”, Nonlinear Analysis: Real World Applications3358–82.

Huang, J., Gong, Y. Ruan, S. 2013. “Bifurcation analysis in a predatorprey model with constant-yield predator harvesting”, Discrete Contin. Dynam. Syst. Ser. B182101–2121.

Kar, TK. 2006. “Modelling and analysis of a harvested preypredator system incorporating a prey refuge”, Journal of Computational and Applied Mathematics 185 (2006) 19 3318519–33.

Kofoid, C. 1925. “Elements of physical biology”,American Public Health Association.

Mahapatra, D. K. (2014). Neuraminidase Inhibitors – For Effective Treatment of Influenza 22 | IJPRT | January – March Mahapatra et al / International Journal of Pharmacy Research & Technology 2014, 4(1), 22–31.

Mukhopadhyay, B. Bhattacharyya, R. 2016. “Effects of harvesting and predator interference in a model of two predators competing for a single prey”, Applied Mathematical Modelling4043264–3274.

Perko, L. 2013. “Differential equations and dynamical systems(7)”, Springer Science & Business Media.

Singh, MK., Bhadauria, B. Singh, BK. 2016. “Qualitative Analysis of a Leslie-Gower Predator-Prey System with Nonlinear Harvesting in Predator”, International Journal of Engineering Mathematics2016.

Sotomayor, J. 1973. “Generic bifurcations of dynamical systems”, Dynamical systems ( 561–582). Elsevier.

Sumich, JL. Morrissey, JF. 2004. “Introduction to the biology of marine life”, Jones & Bartlett Learning.

Toaha, S. Azis, MI. 2018. “Stability and Optimal Harvesting of Modified Leslie-Gower Predator Prey Model”,J. Phys.: Conf. Ser.979012069

Xiao, D., Li, W. Han, M. 2006. “Dynamics in a ratio-dependent predatorprey model with predator harvesting”, J. Math. Anal. Appl.304440314–29.

Yang, R., Zhang, C. 2017. “Dynamics in a diffusive modified Leslie-Gower predatory-prey model with time delayand prey harvesting”, Nonlinear Dynamics. 87: 863.

Zhi-Fen, Z., Tong-Ren, D., Wen-Zao, H. Zhen-Xi, D. 2006. “Qualitative theory of differential equations( 101)”, American Mathematical Soc.

Zhu, C. Lan, K. 2010. “Phase portraits, Hopf bifurcations and limit cycles of Leslie-Gower predator-prey systems with harvesting rates”, Discrete & Continuous Dynamical Systems-B141289–306.



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