Bifurcation Spectral Diagrams: a Tool for Nonlinear Dynamics Investigation

Bifurcation diagram is a commonly used tool to analyze the nonlinear dynamics. It represents the phase space properties of the system. However, the spectral analysis of nonlinear and, particularly, chaotic systems in respect to a varying parameter is often of interest. We show that bifurcation analysis in the frequency domain can be performed using diagrams similar to spectrograms with the bifurcation parameter axis instead of the time axis. Thus, it is possible to reveal the hidden features of the system's behavior in cases where the bifurcation diagrams turn out to be inefficient. This paper provides a basic methodology of this novel approach and demonstrates some results obtained with it.