Bifurcation structure of the Toda oscillator

Abstract
We present phase diagrams of the Toda oscillator x¨+dẋ+ex-1=f cos(ωt) 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.