  A disformal rotating black-hole solution is a black-hole solution in
quadratic degenerate higher-order scalar-tensor theories. It breaks the
circular condition of spacetime different from the case of the usual Kerr
spacetime. This study investigated the dynamic behaviors of the motion of
timelike particles in such disformal black-hole spacetime with an extra
deformation parameter. Results showed that the characteristics of the
particle's motion depend on the sign of the deformation parameter. For the
positive deformation parameter, the motion is regular and orderly. For the
negative one, as the deformation parameter changes, the motion of the particles
undergoes a series of transitions between the chaotic motion and the regular
motion and falls into the horizon or escapes to spatial infinity. This means
that the dynamic behavior of timelike particles in the disformal Kerr
black-hole spacetime with noncircularity becomes richer than that in the usual
Kerr black-hole case.
