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.
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