Open Access Open Access  Restricted Access Subscription or Fee Access

Mathematical Analysis of prey-predator model

A. V. PapaRao, G. A. L. Satyavathi, K. Sobhan Babu


In this paper we considered a model with a prey and predator involve holling type -II functional response. The predator species is not only dependent on prey species but also have alternative food source. The mathematical model is characterized by the couple of differential equations. The model is well posed and possess positive solutions. The system is bounded and shows the property of permeance. The possible equilibrium points are identified. At each point local stability analysis is studied. The global stability analysis is also addressed using Lyapunov’s function approach. The sufficient condition is derived to prove that the system does not admit any periodic oscillations using Bendixen-Dulac criteria. Finally, numerical simulation is performed in support of analytical results.


Prey- predator, local stability, global stability, simulation, mathematical models

Full Text:



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 dition, Springer.

Bandyopadhyay., Chattopadhyay.,2005 Ratio-dependent predator-prey model effect of environmental flucations and stability. Nonlinearity 18(2),913-936.

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.

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

Lakshmi Naryan.K., and Pattabhi,2007, A Prey - Predator Modelwith 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.

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.

Lamontagne, Y., Coutu, C., Rousseau, C.: 2008 Bifurcation analysis of a predator- prey system with generalised Holling type III functional response. J. Dyn. Differ. Equ. 20(3), 535–571.

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.

Sugie, J., Kohno, R., Miyazaki, R.: 1997.On a predator-prey system of Holling type. P. Am. Math. Soc. 125(7), 2041–2050

Sugie, J., Katayama, M.: 1999 Global asymptotic stability of a predator-prey system of Holling type. Nonlinear Anal. Theory. 38(1), 105–121

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

Sita Ram babu. 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 .



  • There are currently no refbacks.