A study on bifurcation diagrams in relation to synchronisation in chaotic systems

Abstract

We numerically study some of the 3-D dynamical systems which exhibit complete synchronisation as well as generalised synchronisation (GS) to show that these systems can be conveniently partitioned into equivalent classes facilitating the study of bifurcation diagrams (BDs) within each class. We demonstrate how BDs may be helpful in assessing the robustness of GS and in predicting the nature of the driven system by knowing the BD of driving system and vice versa. We extend the study to include the possible GS between elements of two different equivalent classes by taking the example of the Rossler-driven-Lorenz-system.