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

Abstract

In this paper, we study the conditions under which the following close‐to‐symmetric system of difference equations with exponential terms: where ai, bi, ci, di, and ki, for , 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.