Stability analysis of Prey- Predator Model with Holling Type-II Response

V.K. Aneela, Paparao A. V

Abstract


In this paper we investigate the dynamics of prey-predator model of holling type II response function. The system is described by a system of ordinary differential equations. The boundedness properties, long term behaviour of the system, equilibrium points are identified. Local stability analysis is discussed at each of its equilibrium points. Global stability is studied by constructing suitable Lyapunov’s function. We proved that the system is both locally and globally asymptotically stable. Further Numerical simulation is performed and in support of analytical study.

Keywords


Prey-predator; Local stability; Global stability; Simulation

Full Text:

PDF

References


Chen, H., Zhang, C.,2022, Analysis of the dynamics of a predator-prey model with holling functional response. J. Nonl. Mod. Anal. 4, 310–324

Carlos Chavez, C., 2012, Mathematical models in population biology and epidemiology, Second Edition, Springer.

Edward A. Bender,1978 Introduction to Mathematical Modelling, John Wiley & Sons,

Freedman.H.I.,1980, Deterministic mathematical models in population ecology, Marcel-Decker, New York.

Gupta, R.P., Chandra, P.,2013, Bifurcation analysis of modified Leslie-Gower predator-prey model with Michaelis-Menten type prey harvesting. J. Math. Anal. Appl. 398(1), 278–295.

Kot, M., 2001,Elements of Mathematical Ecology, Cambridge University press, Cambridge

Lakshmi Naryan.K., and Pattabhi Ramacharyulu.N.ch.,2007, A Prey - Predator Model with cover for Prey and an Alternate Food for the Predator, and Time Delay., International Journal of Scientific Computing, Vol.1 No.1 pp 7-14 .

Lotka. A.J.,1925, Elements of physical biology, Williams and Wilkins, Baltimore.

Liu, W., Jiang, Y.L.,2018, Bifurcation of a delayed gause predator-prey model with Michaelis Menten type harvesting. J. Theor. Biol. 438, 116–132.

Lima, S.L.,1998, Nonlethal effects in the ecology of predator-prey interactions - What are the ecological effects of anti-predator decision-making? Bioscience 48(1), 25–34.

May, R.M.,1973, Stability and complexity in model Eco-Systems, Princeton University press, Princeton.

Murray, J.D.,1989, Mathematical Biology, Biomathematics 19, Springer-Verlag, Berlin-Heidelberg-New York.

Murray, J.D., Mathematical Biology-I.,2002,an Introduction, Third edition, Springer.

Ranjith Kumar Upadhyay, Satteluri R. K. Iyengar.,2014, Introduction to Mathematical Modeling and Chaotic Dynamics, A Chapman & Hall Book, CRC Press.

Ranjith Kumar G, Kalyan Das, Lakshmi Narayan Ravindra Reddy B., 2019,Crowding effects and depletion mechanisms for population regulation in prey-predator intra-specific competition model. Computational Ecology &software ISSN 2220-721Xvol 9 no 1 pp 19-36.

Seo, G., DeAngelis, D.L.,2011, A predator prey model with a Holling type I functional response including a predator mutual interference. J. Nonlinear Sci. 21, 811–833

SreeHariRao.V., and Raja SekharaRao.P.,2009, Dynamic Models and Control of Biological Systems, Springer Dordrecht Heidelberg London New York.

Sita Rambabu. B., Lakshmi Narayan k., 2019, Mathematical Study of Prey-Predator Model with Infection Predator and Intra-specific Competition, International Journal of Ecology & Development ISSN: 0973-7308vol 34 , issue 3(1) pp 11-21 .

Xiao, D.M., Jennings, L.S.,2005, Bifurcations of a ratio-dependent predator-prey system with constant rate harvesting. SIAM J. Appl. Math. 65(3), 737–753.




DOI: http://dx.doi.org/10.21533/scjournal.v12i2.274

Refbacks

  • There are currently no refbacks.


Copyright (c) 2023 V.K. Aneela, Paparao A. V

ISSN 2233 -1859

Digital Object Identifier DOI: 10.21533/scjournal

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License