Study of a predator–prey model with modified Leslie–Gower and Holling type III schemes
- 9 Downloads
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.
KeywordsModified Lesli–Gower model Equilibria Boundedness Stability Persistence
Mathematics Subject Classification92Bxx 92D30 92D40 37B25 34D23
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.
- Birkhoff G, Rota GC (1982) Ordinary differential equations. Ginn, BostonGoogle Scholar
- Gard TC, Hallam TG (1979) Persistece in food web-1, Lotka–Volterra food chains. Bull Math Biol 41:877–891Google Scholar
- Korobeinikovi A (2001) A Lyapunav function for Leslie–Gower prey–predator models. Chaos Solitons Fractals 14:697–699Google Scholar
- Pal PJ, Sarwardi S, Saha T, Mandal PK (2011) Mean square stability in a modified Leslie–Gower and Holling-type II predator–prey model. J Appl Math Inform 29:781–802Google Scholar