Neimark–Sacker, flip, and transcritical bifurcation in a close‐to‐symmetric system of difference equations with exponential terms

In this paper, we study the conditions under which the following close‐to‐symmetric system of difference equations with exponential terms: xn+1=a1ynb1+yn+c1xnek1−d1xn1+ek1−d1xn, yn+1=a2xnb2+xn+c2ynek2−d2yn1+ek2−d2yn where ai, bi, ci, di, and ki, for i=1,2, are real constants and the initial values x...

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Bibliographic Details
Published in:Mathematical methods in the applied sciences 2021-09, Vol.44 (13), p.10210-10224
Main Authors: Mylona, Chrysoula, Papaschinopoulos, Garyfalos, Schinas, Christos J.
Format: Article
Language:English
Subjects:
Bifurcation theory
Canonical forms
center manifold
Difference equations
discrete dynamics
flip bifurcation
Mathematical analysis
Neimark–Sacker bifurcation
Real numbers
transcritical bifurcation
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Summary:In this paper, we study the conditions under which the following close‐to‐symmetric system of difference equations with exponential terms: xn+1=a1ynb1+yn+c1xnek1−d1xn1+ek1−d1xn, yn+1=a2xnb2+xn+c2ynek2−d2yn1+ek2−d2yn where ai, bi, ci, di, and ki, for i=1,2, are real constants and the initial values x0 and y0 are real numbers, undergoes Neimark–Sacker, flip, and transcritical bifurcation. The analysis is conducted applying center manifold theory and the normal form bifurcation analysis.
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.7400