  The nonlinear dynamics of a transverse domain wall (TDW) in Permalloy and
Nickel nanostrips with two artificially patterned pinning centers is studied
numerically up to rf frequencies. The phase diagram frequency - driving
amplitude shows a rich variety of dynamical behaviors depending on the material
parameters and the type and shape of pinning centers. We find that T-shaped
traps (antinotches) create a classical double well Duffing potential that leads
to a small chaotic region in the case of Nickel and a large one for Py. In
contrast, the rectangular constrictions (notches) create an exponential
potential that leads to larger chaotic regions interspersed with periodic
windows for both Py and Ni. The influence of temperature manifests itself by
enlarging the chaotic region and activating thermal jumps between the pinning
sites while reducing the depinning field at low frequency in the notched
strips.
