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Chaotic oscillation of a domain wall is demonstrated by computer simulations based on a differential equation which includes terms for the nonlinear force of restitution and eddy current damping. Chaotic oscillation involves irregular phenomena (the error or noise in magnetic recording systems) and energy losses. Bifurcation diagrams of magnetic domain-wall motion is a useful method for investigating chaotic behavior. The external magnetic field is an important parameter in the design of magnetic devices. The bifurcation diagram of the wall velocity is calculated for the amplitude of the external magnetic field. The route to chaos is through bifurcation via periods 2, 3, 4 and 5 from period-1 oscillation. The periodic windows and chaotic regions appear in alternation. The energy loss caused by the domain wall motion was calculated; the value of the energy loss in chaotic motion is larger than that for regular motion, despite their having the same damping coefficient. Chaotic motion is thus a new mechanism causing increases in the energy loss.