PERIODIC POSITIVE SOLUTIONS OF A DISCRETE FOOD CHAIN PREDATOR-PREY MODEL

Mohammed El Amine Boubekeur, Ahmed Lakmeche, Abdelkader Lakmeche

Abstract


In this work, we investigate a discrete mathematical model describing the evolution of two populations in interaction.
The populations are described by the evolution of three level predator-prey model where the predator feed on both
juvenile and adult preys in different ways. First we prove the existence of periodic positive solution. After that we give
numerical simulations to illustrate our results.


Full Text:

PDF

References


P. A. Abrams and C. Quince, “The impact of mortality on predator population size and stability in systems with stage-structured prey,”

Theoretical Population Biology, vol. 68, no. 4, pp. 253-266, 2005.

L. Chen and F. Chen, ”Positive periodic solution of the discrete Lasota–Wazewska model with impulse,” Journal of Difference Equations and

Applications, vol. 20, no. 3, pp. 406-412, 2014.

J. M. Cushing, “Periodic Time-Dependent Predator-Prey Systems,” SIAM J. Appl. Math.,vol 32, no. 1, pp. 82-85, 1977.

R. E. Gaines and J. L. Mawhin, Coincidence Degree and Nonlinear Differential Equations. Berlin: Springer-Verlag, 1977.

S. A. Gourley and Y. Kuangy, “A stage structured predator-prey model and its dependence on through-stage delay and death Rate,” Journal of

Mathematical Biology, vol. 49, no. 2, pp. 188-200, 2004.

V. Madhusudanan, K. Anitha , S. Vijaya and M. Gunasekaran, ”Complex effects in discrete time prey-predator model with harvesting on prey”

I.J.E.S, vol.3, no.4, pp. 1-5, 2014.

B. Mukhopadhyay and R. Bhattacharyya, “A stage-structured food chain model with stage dependent predation: Existence of codimension one

and codimension two bifurcations,” Nonlinear Analysis: Real World Applications, vol. 12, no. 6, pp. 3056-3072, 2011.-3072

S.M.S. Rana, ”Chaotic dynamics in a discrete-time predator-prey food chain,” Computational Ecology and Software, vol. 5, no. 1, pp. 28-47,

A.G.M. Selvam, R. Janagaraj and P. Rathinavel, ”A discrete model of three species prey-predator system,” IJIRSET, vol. 4, no. 1, pp. 18576-

, 2015.

C. Xu and M. Wang, “Permanence for a delayed discrete three-level food-chain model with Beddington-DeAngelis functional response,”

Applied Mathematics and Computation, vol. 187, no. 2, pp. 1109-1119, 2007.

R. Y. Zhang, Z.C. Wang, Y. Chen and J. Wu, “Periodic solutions of a single species discrete population model with periodic harvest/stock,”

Comput. Math. Appl., vol. 39, no.1, pp. 77-90, 2000.

L. Zou, Z. Xiong and L. Wu, “Stability and permanence of a delayed stage-structured predator-prey system,” in IEEE Conference Publications

, 4th International Conference on Bioinformatics and Biomedical Engineering, pp. 1-4.

X. Zhang, Q. L. Zhang and V. Sreeram, “Bifurcation analysis and control of a discrete harvested prey-predator system with Beddington-

DeAngelis functional response,” Journal of the Franklin Institute, vol. 347, no. 7, pp. 1076-1096, 2010.


Refbacks

  • There are currently no refbacks.


MAYFEB Journal of Mathematics 
Toronto, Ontario, Canada
MAYFEB TECHNOLOGY DEVELOPMENT
ISSN 2371-6193