Modeling Earth Systems and Environment

, Volume 4, Issue 2, pp 527–533

# Study of a predator–prey model with modified Leslie–Gower and Holling type III schemes

• Absos Ali Shaikh
• Harekrishna Das
• Nijamuddin Ali
Original Article

## Abstract

A mathematical model of predator–prey system is studied analytically as well as numerically. The objective of this paper is to study systematically the dynamical properties of a modified Leslie–Gower predator–prey model with Holling type III functional response. We discuss different types of system behaviours for various parameter values. The essential mathematical features of the model with regard to the boundedness, stability and persistence have been carried out. Some numerical simulations are carried out to support our theoretical analysis. All the results are expected to be of use in the study of the dynamic complexity of ecosystem.

## Keywords

Modified Lesli–Gower model Equilibria Boundedness Stability Persistence

## Mathematics Subject Classification

92Bxx 92D30 92D40 37B25 34D23

## Notes

### Acknowledgements

The authors express their sincere thanks to the reviewer for valuable suggestions towards the improvement of the paper. The second author is grateful to ICCR (Indian Council for Cultural Relations), New Delhi (File no. 6-44/2015-16/ISD-II) for awarding the scholarship.

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© Springer International Publishing AG, part of Springer Nature 2018

## Authors and Affiliations

• Absos Ali Shaikh
• 1
• Harekrishna Das
• 1
• Nijamuddin Ali
• 2
1. 1.Department of MathematicsThe University of BurdwanBurdwanIndia
2. 2.Department of MathematicsKatwa College (B.Ed. Section)BurdwanIndia