Deterministic diffusion generated by a chaotic map with intrinsic bias

We investigate diffusive motion that results from random walks generated by the deterministic Kim–Kong map. The orbital density is not symmetric in this map and random walks generated by the map have an intrinsic bias. An external bias parameter is adjusted to compensate this intrinsic bias so that the average step length of walkers vanishes. The mean square displacement of diffusing walkers is computed for parameter values in the chaotic window and is found to scale linearly with time for typical parameter values, including the reverse bifurcation point and the end of the chaotic window. For parameter values near the period three cycle, where the orbit alternates intermittently between regular and irregular behaviours, normal diffusion occurs after the elapse of an initial transient time.