Routes to suppressing chaos by weak periodic perturbations

A new route is described for eliminating chaos in nonlinear oscillators by changing only the shape of a weak nonlinear periodic perturbation and illustrated with the example of the Duffing-Holmes oscillator forced with the Jacobian elliptic function sn. Two techniques are used in the illustration: applying the Melnikov-Holmes analysis, and studying the behavior of the Lyapunov exponent from a simple recursion relation which models an unstable limit cycle. The connection with related previously described routes is also discussed in a general setting.