Dynamic Behavior and Bifurcation Analysis of a Difference Equation Including Exponential Terms

Elsadany, A.A.; Ibrahim, Samia; Elabbasy, E. M.

doi:10.28919/cpr-pajm/3-14

Research article

Dynamic Behavior and Bifurcation Analysis of a Difference Equation Including Exponential Terms

A.A. Elsadany, Samia Ibrahim, E. M. Elabbasy

Abstract

In this paper, the local stability, the boundedness, rate of convergence and the conditions of Neimark-Sacker bifurcation concerning difference equation
x_n+1=α₁x_n+α₂x_n_-1+β₁x_nexp(-x²_n_-1)+β₂x_n_-1exp(-x²_n_-1), n=0,1, ...,
are investigated. We focus on the Neimark-Sacker bifurcations of the discrete model. The center manifold theorem and bifurcation theory are explicitly applied to reach conclusions about the occurrence and stability of the Neimark-Sacker bifurcation. Many numerical simulations that confirm the existence of the Neimark-Sacker bifurcation are also provided.

How to cite

A. A. Elsadany, S. Ibrahim, E. M. Elabbasy, Dynamic Behavior and Bifurcation Analysis of a Difference Equation Including Exponential Terms, Pan-Amer. J. Math. 3 (2024), 14. https://doi.org/10.28919/cpr-pajm/3-14

BibTeX

@article{Elsadany2024,
  author  = {Elsadany, A.A. and Ibrahim, Samia and Elabbasy, E. M.},
  title   = {Dynamic Behavior and Bifurcation Analysis of a Difference Equation Including Exponential Terms},
  journal = {Pan-Amer. J. Math.},
  volume  = {3},
  year    = {2024},
  pages   = {14},
  doi     = {10.28919/cpr-pajm/3-14}
}