DYNAMIC BEHAVIOR AND BIFURCATION ANALYSIS OF A DIFFERENCE EQUATION INCLUDING EXPONENTIAL TERMS

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

doi:10.28919/cpr-pajm/3-14

DYNAMIC BEHAVIOR AND BIFURCATION ANALYSIS OF A DIFFERENCE EQUATION INCLUDING EXPONENTIAL TERMS

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

Mathematics

Research output: Contribution to journal › Article › peer-review

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 = α₁ x_n + α₂ x_n−1 + β₁ x_n exp(−x²_n−1) +β₂x_n−1 exp(−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.

Original language	English
Article number	14
Journal	Pan-American Journal of Mathematics
Volume	3
DOIs	https://doi.org/10.28919/cpr-pajm/3-14
State	Published - 2024

Keywords

Center manifold
Neimark-Sacker bifurcation
Rational difference equation
Stability

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title = "DYNAMIC BEHAVIOR AND BIFURCATION ANALYSIS OF A DIFFERENCE EQUATION INCLUDING EXPONENTIAL TERMS",

abstract = "In this paper, the local stability, the boundedness, rate of convergence and the conditions of Neimark-Sacker bifurcation concerning difference equation xn+1 = α1 xn + α2 xn−1 + β1 xn exp(−x2n−1) +β2xn−1 exp(−x2n−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.",

keywords = "Center manifold, Neimark-Sacker bifurcation, Rational difference equation, Stability",

author = "Elsadany, \{A. A.\} and Samia Ibrahim and Elabbasy, \{E. M.\}",

note = "Publisher Copyright: {\textcopyright} 2024 by the authors.",

year = "2024",

doi = "10.28919/cpr-pajm/3-14",

language = "English",

volume = "3",

journal = "Pan-American Journal of Mathematics",

issn = "2832-4293",

publisher = "Mathyze Publishers",

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TY - JOUR

T1 - DYNAMIC BEHAVIOR AND BIFURCATION ANALYSIS OF A DIFFERENCE EQUATION INCLUDING EXPONENTIAL TERMS

AU - Elsadany, A. A.

AU - Ibrahim, Samia

AU - Elabbasy, E. M.

PY - 2024

Y1 - 2024

N2 - In this paper, the local stability, the boundedness, rate of convergence and the conditions of Neimark-Sacker bifurcation concerning difference equation xn+1 = α1 xn + α2 xn−1 + β1 xn exp(−x2n−1) +β2xn−1 exp(−x2n−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.

AB - In this paper, the local stability, the boundedness, rate of convergence and the conditions of Neimark-Sacker bifurcation concerning difference equation xn+1 = α1 xn + α2 xn−1 + β1 xn exp(−x2n−1) +β2xn−1 exp(−x2n−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.

KW - Center manifold

KW - Neimark-Sacker bifurcation

KW - Rational difference equation

KW - Stability

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U2 - 10.28919/cpr-pajm/3-14

DO - 10.28919/cpr-pajm/3-14

M3 - Article

AN - SCOPUS:85202529097

SN - 2832-4293

VL - 3

JO - Pan-American Journal of Mathematics

JF - Pan-American Journal of Mathematics

M1 - 14

ER -

DYNAMIC BEHAVIOR AND BIFURCATION ANALYSIS OF A DIFFERENCE EQUATION INCLUDING EXPONENTIAL TERMS

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Keywords

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