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Communications in Mathematical Biology and Neuroscience ISSN 2052-2541

Archives › Volume 2022 (2022)

Commun. Math. Biol. Neurosci. 2022 (2022), Article ID 61

Stability analysis and Neimark-Sacker bifurcation of a nonstandard finite difference scheme for Lotka-Volterra prey-predator model

R. Ahmed, A. Ahmad, N. Ali

PDF (903.2 KB) https://doi.org/10.28919/cmbn/7534

Abstract

To discretize the Lotka-Volterra prey-predator model, we adopted a dynamically consistent nonstandard finite difference scheme. The existence of fixed points and their topological categorization are examined. It is proved using bifurcation theory that the system experiences Neimark-Sacker bifurcation. Moreover, the hybrid control method is used to control the Neimark-Sacker bifurcation. Additionally, numerical simulations are performed to show the system’s complexity and consistency with analytical results.

Published
4 July 2022
Volume
2022 (2022)
License
CC BY 3.0

Copyright © 2022 R. Ahmed, A. Ahmad, N. Ali. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Cite this article

R. Ahmed, A. Ahmad, N. Ali, Stability analysis and Neimark-Sacker bifurcation of a nonstandard finite difference scheme for Lotka-Volterra prey-predator model, Commun. Math. Biol. Neurosci. 2022 (2022), 61. https://doi.org/10.28919/cmbn/7534

BibTeX
@article{Ahmed2022,
  author  = {Ahmed, R. and Ahmad, A. and Ali, N.},
  title   = {Stability analysis and Neimark-Sacker bifurcation of a nonstandard finite difference scheme for Lotka-Volterra prey-predator model},
  journal = {Commun. Math. Biol. Neurosci.},
  volume  = {2022},
  year    = {2022},
  pages   = {61},
  doi     = {10.28919/cmbn/7534}
}