The differential steering-by-wire (DSBW) system eliminates the need for steering
                    gear, i.e., rack and pinion, while preserving a trapezoidal steering structure
                    with knuckles. This design offers significant advantages for vehicles equipped
                    with in-wheel motors, primarily due to reduced vehicle weight and the
                    maintenance of front wheel alignment parameters. However, the noise force acting
                    on one steering wheel will directly transmit to the other in this differential
                    steering mechanism due to a lack of mechanical connection to the vehicle body
                    through the steering gear, which increases the risk of steering wheel shimmy
                    (SWS). This article qualitatively analyzes the shimmy characteristics of the
                    steering wheel based on a three-degrees-of-freedom (3-DOF) DSBW shimmy model
                    established using Lagrange’s equation and the Hopf bifurcation theorem. The
                    results indicate the vehicle range that this steering system will shimmy, and
                    the maximum steady amplitude is [4.80 m/s, 31.57 m/s] and 0.1516 rad,
                    respectively, much bigger than those of the traditional steering systems
                    incorporating steering gear. Key parameters, such as wheel weight, half the
                    length of tire patch, and caster angle, are found to substantially affect the
                    shimmy characteristics of the steering system. Furthermore, the stiffness and
                    damping coefficients of the tie rod influence the phase offset of the steering
                    angle between the left and right wheels, whereas the effects of other
                    parameters, including the stiffness and damping coefficients of the suspension,
                    are relatively minor.