Bifurcation structure of the Toda oscillator.

Abstract

We present phase diagrams of the Toda oscillator x\ifmmode\ddot\else\textasciidieresis\fi{}+dx\ifmmode \dot{}\else \.{}\fi{}+${e}^{x}$-1=f cos(\ensuremath{\omega}t) showing the loci of local bifurcations of periodic orbits in the (\ensuremath{\omega},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.