COMPLEX DYNAMICS IN 2-SPECIES PREDATOR-PREY SYSTEMS

I. Djellit; M. L. Sahari; A. Hachemi

doi:10.11948/2013002

2013 Volume 3 Issue 1

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I. Djellit, M. L. Sahari, A. Hachemi. COMPLEX DYNAMICS IN 2-SPECIES PREDATOR-PREY SYSTEMS[J]. Journal of Applied Analysis & Computation, 2013, 3(1): 11-20. doi: 10.11948/2013002

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I. Djellit, M. L. Sahari, A. Hachemi. COMPLEX DYNAMICS IN 2-SPECIES PREDATOR-PREY SYSTEMS[J]. Journal of Applied Analysis & Computation, 2013, 3(1): 11-20. doi: 10.11948/2013002

COMPLEX DYNAMICS IN 2-SPECIES PREDATOR-PREY SYSTEMS

1 Laboratory of Mathematics, Dynamics and Modelization, University Badji Mokhtar-Annaba, Annaba, Algeria;
2 Laboratory of Quantic Physics and Dynamical Systems, University Ferhat Abbas, Setif, Algeria

Abstract

Abstract

In this work, we consider some dynamical properties and specific contact bifurcations of a discrete-time predator-prey system having inverses with vanishing denominator. The dynamics is investigated by using concepts of focal points, prefocal curves and bifurcation theory. The system undergoes flip bifurcation and Neimark-Sacker bifurcation. Numerical simulations are presented not only to illustrate our results with the theoretical analysis, but also to confirm further the complexity of the dynamical behaviors as extinction, persistence and permanence.
- Prey-predator system /
- bifurcation basin /
- map with denominator /
- focal point
MSC: 34D45;37G35;37D45

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References

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