Bifurcation structure of the Toda oscillator

We present phase diagrams of the Toda oscillator x{}+dx ̇ \.{}{}+eˣ-1=f cos({ω}t) showing the loci of local bifurcations of periodic orbits in the ({ω},f) parameter plane at d=0.05. They indicate a specific recurrent structure in the bifurcation set which is typical for nonlinear oscillators and closely connected to the nonlinear resonances of the system.