Volume 2 | Issue 3 | Year 2011 | Article Id. IJMTT-V2I3P507 | DOI : https://doi.org/10.14445/22315373/IJMTT-V2I3P507
We present a mathematical model for preypredator model. We assume that the interaction is nonlinear and of third order. We discuss in detail the stability of the critical points.
[1] Abulwafa, E.M., Abdou, M.A. and Mahmoud, A.A., 2006.The solution of nonlinear coagulations problem with mass loss, Chaos, Solution and Fractals, in press
[2] Beddington, J.R., Free, C.A., Lawton, J.H. (1975). Dynamic Complexity in Predator-prey Models Framed in difference equations. Journal of Nature 255, 58-60.
[3] Dunbar, S.R. (1984). Traveling wave Solutions of diffusive Lokta-Volterra equations. Journal of Mathematical Biology, 17, 11-32.
[4] Dunbar, S.R. (1984). Traveling wave Solutions of diffusive Lokta-Volterra equations: A Heteroclinic connection in R4 .Trans. American Mathematical Society, 268, 557-594.
[5] Francis Benyah (2008). Introduction to Epidemiological modeling.10th Regional College on Modelling, Simulation and Optimization.
[6] Hoppensteadt, F. (2006). Predator-prey Model Scholarpedia (the free peer-reviewed encyclopedia) p.5765-5772.Available on line (http://www.scholarpedia.org/article/predator-prey_model)
[7] Khaled Batiha., 2007.Numerical solutions of the Multispecies Predator-Prey Model by Variational Iteration Method.
[8] May, R.M. and Leonard W.J., 1975.Nonlinear aspects of competition between three species. SIAM J.Appl.Math. 29:243-253.
[9] Murray, J.D. (1989). Mathematical Biology, 2nd Edition. Springer-Verlag, New York 72-78.
[10] Murray, J.D. (1989). Mathematical Biology, 2nd Edition. Springer-Verlag, New York 78-83.
[11] Olek S., 1994.An accurate solution to the multispecies Lokta-Volterra equations. SIAM Review, 36:480-488.
[12] S. Pathak et al.(2010). Rich Dynamics of an SIR epidemic Model. Vol. 15 Nonlinear Analysis: Modelling and Control, 71-81.
[13] Simeon, C.I., (2008). Predator-prey mathematical model using Van Der Pol’s equation. Journal of Nigerian Association of Mathematical Physics. Volume 12 (May, 2008), 435-438
[14] Smith, H. and Waltman, P. (1997).The Mathematical Theory of Chemostats, Cambridge University Press.
[15] Volterra, V. (1926). Variations and Fluctuations of a number of individuals in animal species living together.[In R.N. Animal Ecology, New York, McGraw Hill, 1931, 409-448]
Bakare E.A, Adekunle Y.A, Kadiri K.O, "A Prey-Predator Model with Third order Interaction," International Journal of Mathematics Trends and Technology (IJMTT), vol. 2, no. 3, pp. 30-33, 2011. Crossref, https://doi.org/10.14445/22315373/IJMTT-V2I3P507