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Neimark–Sacker, flip, and transcritical bifurcation in a close‐to‐symmetric system of difference equations with exponential terms
Author(s) -
Mylona Chrysoula,
Papaschinopoulos Garyfalos,
Schinas Christos J.
Publication year - 2021
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.7400
Subject(s) - mathematics , center manifold , transcritical bifurcation , exponential function , bifurcation , mathematical analysis , saddle node bifurcation , pitchfork bifurcation , bifurcation diagram , hopf bifurcation , nonlinear system , physics , quantum mechanics
In this paper, we study the conditions under which the following close‐to‐symmetric system of difference equations with exponential terms:x n + 1 = a 1y nb 1 + y n+ c 1x nek 1 − d 1x n1 + ek 1 − d 1x n,y n + 1 = a 2x nb 2 + x n+ c 2y nek 2 − d 2y n1 + ek 2 − d 2y nwhere a i , b i , c i , d i , and k i , for i = 1,2 , are real constants and the initial values x 0 and y 0 are real numbers, undergoes Neimark–Sacker, flip, and transcritical bifurcation. The analysis is conducted applying center manifold theory and the normal form bifurcation analysis.