Dynamics of coupled non-identical systems with period-doubling cascade

TL;DR

This paper investigates the bifurcation structure and chaos transition in coupled logistic maps, identifying a codimension-two critical point and analyzing bifurcations near this point using Lyapunov exponents.

Contribution

It provides a detailed bifurcation analysis of coupled logistic maps, including the identification of a critical codimension-two point at the chaos boundary.

Findings

Identification of a codimension-two critical point at the chaos border.

Charts of dynamical regimes and Lyapunov exponents illustrating bifurcation structures.

Analysis of bifurcations near the critical point.

Abstract

Structure of bifurcation diagram in the plane of parameters controlling period-doublings for the system of coupled logistic maps is discussed. The analysis is carried out by computing the charts of dynamical regimes and charts of Lyapunov exponents giving showy and effective illustrations. The critical point of codimension two at the border of chaos is found. It is a terminal point for the Feigenbaum critical line. The bifurcation analysis in the vicinity of this point is presented.