We use a mathematical model to investigate the early temporal dynamics of motion integration with a multistable input. A drifting grating stimulus is considered with an aperture configuration that supports horizontal (H), diagonal (D) or vertical (V) perceived directions for the same input. A shift in perceptual dominance from D to either H/V with increased presentation duration has been shown in short-presentation psychophysics experiments; see our companion abstract (I). We work with a neural fields, population-level representation of cortical activity that performs motion integration of the competing oblique (D) and cardinal (H/V) local direction signals [Rankin et al., 2011, INRIA Report 7822]. When a dynamical system diverges away from a weakly unstable state it can spend an extended transient period close to the unstable state before divergence [Strogatz, 2001, Nonlinear Dynamics and Chaos, Perseus, NY]. Of the competing states representing the alternative percepts, the initially dominant D is computed to be weakly unstable whilst the subsequently dominant H/V are computed to be stable. The property of weak stability explains the gradual shift in dominance from D to H/V. Moreover, as contrast increases, D becomes strongly unstable reducing the latency of this shift in perceptual dominance.