Dynamics Analysis of Modified Leslie-Gower Model with Simplified Holling Type IV Functional Response

Authors

  • Nur Suci Ramadhani Hasanuddin University
  • Toaha Toaha Hasanuddin University
  • Kasbawati Kasbawati Hasanuddin University

DOI:

https://doi.org/10.20956/j.v18i1.13881

Keywords:

Predator-Prey, Modified Leslie-Gower Model, Functional Response, Simplified Holling Type IV

Abstract

In this paper, the modified Leslie-Gower predator-prey model with simplified Holling type IV functional response is discussed. It is assumed that the prey population is a dangerous population. The equilibrium point of the model and the stability of the coexistence equilibrium point are analyzed. The simulation results show that both prey and predator populations will not become extinct as time increases. When the prey population density increases, there is a decrease in the predatory population density because the dangerous prey population has a better ability to defend itself from predators when the number is large enough.

Downloads

Download data is not yet available.

Author Biographies

Toaha Toaha, Hasanuddin University

Department of Mathematics Hasanuddin University

Kasbawati Kasbawati, Hasanuddin University

Departement of Mathematics Hasanuddin University

References

Alaoui, M. A. & Okiye D., 2003. Boundedness and Global Stability for a Predator-Prey Model with Modified Leslie-Gower and Holling-Type II Schemes. Applied Mathematics Letter, 1069 – 1075.

Alaoui, M. A., 2002. Study of a Leslie-Gower Type Tritrophic Population. Chaos Soliton Fract,Vol. 2002, No. 14 , 1275 – 1293.

Andrews, J. A., 1968. The Effect of Enrichment of Three Species Food Chain with Nonlinear Functional Response. Biotechnology and Bioengineering, Vol. 10, No. 6, 707 – 723.

Chen L. & Chen F., 2009. Global Stability of a Leslie-Gower Model with Feedback Controls. Applied Mathematics Letters, Vol. 22, No. 9, 1330 – 1334.

Feng P.& Kang Y., 2015. Dynamics of a Modified Leslie-Gower Model with Double Allee Effects. Nonlinear Dynamics, 80: 1051 – 1062.

Huang J., Xiaojing X. & Xinan Z., 2016. Bifurcation of Codimension 3 in a Predator-Prey System of Leslie Type with Simplified Holling Type IV Functional Response. International Jurnal of Bifurcation and Chaos, Vol. 26, No. 2, 1650034 – 11.

Huang, To, Huayong Z., Zhengran H., Ge P., Shengnan M., Xiumin Z. & Zichun G., 2019. Predator-Prey Pattern Formation Driven by Population Diffusion Based on Moore Neighborhood Structure. Advances in Difference Equation, 399.

Khajanchi S., 2017. Modeling the Dynamics of Stage-Structure Predator-Prey System with Monod-Haldane Type Response Function. Applied Mathematics and Computations, 302: 122 – 143.

Liu M. & Wang K. 2013. Dynamics of a Leslie-Gower Holling Type II Predator-Prey System with Levy Jumps. Nonlinear Analysis: Theory, Methods & Applications, Vol 85, 204 – 213.

Ruan, S. dan Dongmei X., 2001. Global Analysis in A Predator-Prey System with Nonmonotonic Functional Response. SIAM J. APPL. MATH, Vol. 61, No. 4, 1445 –1472.

Shen, C., 2007. Permanence and Global Attractivity of Food-Chain System with Holling IV Type Functional Response. Applied Mathematics and Computations, 194: 179 – 185.

Siddik, A. M. A., dkk. 2021. Stability analysis of Prey-Predator Model with Holling Type IV Functional Response and Infectious Predator. Jurnal Matematika, Statistika & Komputasi, Vol. 17, No. 2, 155 – 165.

Sokol, W. & Howel, J. A., 1987. The Kinetics of Phenol Oxidation by Washed Cells. Biotechnology and Bioengineering, 30: 921 – 927.

Song, J., dkk. 2019. A Non-Autonomous Leslie-Gower Model with Holling Type IV Functional Response and Harvesting Complexity. Advances in Difference Equation, 2019: 299.

Xu D., Liu M. & Xu X., 2020. Analysis of Stochastic Predator-Prey System with Modified Leslie-Gower Model and Holling Type IV Schemes. Physica A, Vol. 2020, No. 537, 122761.

Yu S., 2014. Global Stability of a Modified Leslie-Gower Model with Beddington-DeAngelis Functional Response. Advances in Difference Equation, 2014: 84.

Yusrianto, dkk. 2019. Analisis Kestabilan Model Mangsa Pemangsa dengan Pemanenan Ambang Batas pada Populasi Pemangsa. Jurnal Matematika, Statistika & Komputasi, Vol. 16, No. 1, 97 – 106.

Yue Q., 2016. Dynamics of Modified Leslie-Gower Model Predator-Prey Model with Holling Type II Schemes and a Prey Refuge. Springer Plus, 5: 461.

Zhang Z., Upadhyay R. K. & Datta J., 2018. Bifurcation Analysis of a Modified Leslie-Gower Model with Holling Type IV Functional Response and Nonlinear Prey Harvesting. Advances in Difference Equation, 2018: 127.

Downloads

Published

2021-09-02

How to Cite

Ramadhani, N. S., Toaha, T., & Kasbawati, K. (2021). Dynamics Analysis of Modified Leslie-Gower Model with Simplified Holling Type IV Functional Response. Jurnal Matematika, Statistika Dan Komputasi, 18(1), 12-21. https://doi.org/10.20956/j.v18i1.13881

Issue

Section

Research Articles

Most read articles by the same author(s)

1 2 > >>