| Issue |
Math. Model. Nat. Phenom.
Volume 15, 2020
Ecology and evolution
|
|
|---|---|---|
| Article Number | 60 | |
| Number of page(s) | 27 | |
| DOI | https://doi.org/10.1051/mmnp/2020042 | |
| Published online | 03 December 2020 | |
A class of discrete predator–prey interaction with bifurcation analysis and chaos control
1
Department of Mathematics, University of Poonch Rawalakot,
Azad Kashmir, Pakistan.
2
Department of Mathematics, Air University,
Islamabad, Pakistan.
* Corresponding author: qamar.sms@gmail.com
Received:
10
March
2020
Accepted:
11
September
2020
The interaction between prey and predator is well-known within natural ecosystems. Due to their multifariousness and strong link population dynamics, predators contain distinct features of ecological communities. Keeping in view the Nicholson-Bailey framework for host-parasitoid interaction, a discrete-time predator–prey system is formulated and studied with implementation of type-II functional response and logistic prey growth in form of the Beverton-Holt map. Persistence of solutions and existence of equilibria are discussed. Moreover, stability analysis of equilibria is carried out for predator–prey model. With implementation of bifurcation theory of normal forms and center manifold theorem, it is proved that system undergoes transcritical bifurcation around its boundary equilibrium. On the other hand, if growth rate of consumers is taken as bifurcation parameter, then system undergoes Neimark-Sacker bifurcation around its positive equilibrium point. Methods of chaos control are introduced to avoid the populations from unpredictable behavior. Numerical simulation is provided to strengthen our theoretical discussion.
Mathematics Subject Classification: 39A30 / 40A05 / 92D25 / 92C50
Key words: Predator–prey model / stability / transcritical bifurcation / Neimark-Sacker bifurcation / chaos control
© The authors. Published by EDP Sciences, 2020
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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