• Himmatul Ulya Febriyanti Hasanuddin University
  • Syamsuddin Toaha Hasanuddin University
  • Kasbawati Kasbawati Hasanuddin University



leslie-gower, holling III, bionomic equilibrium, maximum pontryagin policy


This article modified the leslie-gower model on harvesting with predator and prey population. This study aims at construct a modification of leslie-gower model with holing III response function. In addition, there is an effort harvesting in predator and prey population, analyzing an equilibrium point, finding bionomic equilibrium and the condition where the present value is maximum from net income by controlling harvesting in both populations. In the modified leslie-gower model there is an equilibrium point  which is asymptotically stable and when there have harvesting, the equilibrium point  is also asymptotically stable. Bionomic equilibrium from harvesting on the modified leslie-gower model is maximizing the profit function π of harvesting on a model with the maximum pontryagin principle resulting an optimal equilibrium) affected by instantaneous rate of discount δ.


Download data is not yet available.


Ashine, Ahmed Buseri dan Dawit Melese Gebru, 2017. Mathematical Modeling of a Predator-Prey Model with Modified Leslie-Gower and Holling-Type II Schemes. Mathematics and Decision Sciences. 17: 20-40.

Ávila-Vales, Eric, dkk. 2017. Bifurcations of a Leslie-Gower Predator-Prey Model with Holling Type III functional Response and Michaelis-Menten Prey Harvesting.

Barnett, S., 1971. A New Formulation of The Theorems of Hurwitz, Routh and Sturm. J. Inst. Maths Applics. 8: 240-250.

Berryman, Alan. A. 1992. The Origins and Evolution of Predator-Prey Theory. Ecology. Amerika. 73: 1530-1535

Boyce, William E dan Richard DiPrima. 2012. Elementary Differential Equations and Boundary Value Problems. Wiley & Sons: Amerika.

Chen, Fengde, dkk. 2017. Dynamic Behaviors Nonautonomous Modified Leslie-Gower Predator-Prey Model with Holling Type III Schemes and a Prey Refuge. Journal of Mathematics and Computer Science. 17: 266-277Clark, Colin W. 2006. The Worldwide Crisis in Fisheris. Cambridge University Press: Inggris.

Didiharyono., 2016. Analisis Kestabilan dan Keuntungan Maksimum Model Predator-Prey Fungsi Respon Tipe Holling III dengan Usaha Pemanenan. Masagena Jurnal. 11: 314-326.

Huang, Jicai, Shigui Ruan dan Jing Song., 2014. Bifurcations in a Predator-Prey System of Leslie Type With Generalized Holling Type III functional response. Journal of Differential Equations.

Kempf, Alexander., 2008. Predator-Prey Overlap Induced Holling Type III Functional Response in The North Sea Fish Assemblage . Marine Ecology Progress Series. 367: 295-308.

Keshet, Leah Edelstain. 2005. Mathematical Models in Biology. SIAM: Amerika.

Khalil, Hassan K., 2002. Nonlinear Systems Third Edition. Prentice Hall: Amerika.

Lenhart, Suzanne dan John T. Workman., 2007. Optimal Control Applied and Biological Models. CRC Press: New York.

Leslie, P.H. dan J. C. Gower. 1960. The Properties of a Stochastic Model for The Predator-Prey Type of Interaction Between Two Species. Biometrika. 47: 219-234.

Maziun, Nur Aina, dkk., 2010. “Analisis Stabilitas Lokal dan Kontrol Optimal Pada Terapi Obat Dalam Pengobatan Kanker”. ITS Library.

Naidu, D. S., 2002. Optimal Control Systems. CRC Presses LLC: Amerika.

Prastiwi, Lusiana dan Subiono. “Aplikasi Prinsip Maksimum Pontryagin Pada Model Bioekonomi Prey-Predator dengan Waktu Tunda”. Prosiding Seminar FMIPA UNS. Surabaya, 24 Januari 2012.

Shaikh, Absos Ali, dkk. Study of LG Holling Type III Predator-Prey Model with Diseas in Predator. Journal of Mathematics and Computing. 1-21.

Sharma, Anuj. K, dkk., 2014. “Dynamical Analysis of a Harvesting Model of Phytoplankton-Zooplankton Interaction”. International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering. 8: 1013-1018.

Sinclair, A. R. E, dkk. 1998. ,“Prediciting Effect of Predation of Conservation of Endangered Prey”. Conservation Biology. 12: 564-575.

Taha, Hamdy. A. 2007., Operations Research: An Introduction Eight Edition. Pearson Education: Amerika.

Thomas, George B., 2014. Calculus Early Transcendentals Thirteenth Edition. Pearson Education: Amerika.

Wiggins, Stephen., 2003. Introduction to Applied Nonlinear Dynamical Systems and Chaos. Springer: Amerika.

Yang, Wensheng dan Yongqing Li., 2013. “Dynamics of a Diffusive Predator-Prey Model with Modified Leslie- Gowwer and Hollig Type III Scjemes”. Computers, Mathematics and Applications. 65: 1727-1737.

Yue, Qin. ,2016. “Dynamics of Modified Leslie-Gower Predator-Prey Model with Holling Type II Schemes and Prey Refuge”. Springer Plus. 5: 1-12.

Toaha, S dan M I Azis., 2018. Stability and Optimal Harvesting of Modified Leslie-Gower Predator-Prey Model. Journal of Physics. 979: 1-9.






Research Articles

Most read articles by the same author(s)

1 2 3 4 > >>