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.

General results concerning maintenance or enhancement of chaos are presented for dissipative systems subjected to two harmonic perturbations (one chaos inducing and the other chaos enhancing). The connection with previous results on chaos suppression is also discussed in a general setting. It is demonstrated that, in general, a second harmonic perturbation can reliably play an enhancer or inhibitor role by solely adjusting its initial phase. Numerical results indicate that general theoretical findings concerning periodic chaos-inducing perturbations also work for aperiodic chaos-inducing perturbations, and in arrays of identical chaotic coupled oscillators.

It is shown that, depending on its amplitude, frequency, and initial phase, a time-dependent periodic parametric perturbation can suppress chaos in nonlinear oscillators. The example of the Duffing-Holmes oscillator is used to demonstrate that all the numerically and experimentally observed phenomenology is theoretically explained by using the Melnikov-Holmes method and suppression of chaos is seen to be possible when certain resonant frequencies are involved.

We demonstrate that directed transport of topological solitons in damped, biharmonically driven Frenkel-Kontorova chains can be strongly enhanced by introducing suitable phase disorder into the asymmetric periodic driving. From a collective coordinate formalism, we theoretically deduce an effective deterministic equation of motion governing the dynamics of the soliton center-of-mass for which we predict the dependence of maximal soliton drift on disorder strength according to recently proposed general scaling laws concerning directed transport induced by symmetry breaking of temporal forces. We find that these results are in excellent agreement with those of computer simulations of the original Frenkel-Kontorova chains.

We study analytically and numerically the motion of a trapped two-level ion in the presence of a resonant laser field. Using a semiclassical description, we find that for sufficiently strong laser fields atomic motion becomes chaotic for a wide range of parameters and initial conditions. The traces of chaotic motion are reflected in the population inversion of the trapped ion, and thus could be observed by using the quantum jump technique.