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Abstract

Periodic forcing is introduced into the Lorenz model to study the effects of time-dependent forcing on the behavior of the system. Such a
nonautonomous system stays dissipative and has a bounded attracting set which all trajectories finally enter. The possible kinds of attracting sets are
restricted to periodic orbits and strange attractors. A large-scale survey of parameter space shows that periodic forcing has mainly three effects in the
Lorenz system depending on the forcing frequency: (i) Fixed points are replaced by oscillations around them; (ii) resonant periodic orbits are created
both in the stable and the chaotic region; (iii) chaos is created in the stable region near the resonance frequency and in periodic windows. A
comparison to other studies shows that part of this behavior has been observed in simulations of higher truncations and real world experiments. Since very
small modulations can already have a considerable effect, this suggests that periodic processes such as annual or diurnal cycles should not be omitted even
in simple climate models.