Memory-induced anomalous dynamics: Emergence of diffusion, subdiffusion, and superdiffusion from a single random walk model.
We present a random walk model that exhibits asymptotic subdiffusive, diffusive, or superdiffusive behavior in different parameter regimes. This appears to be an instance of a single random walk model leading to all three forms of behavior by simply changing parameter values. Furthermore, the model offers the great advantage of analytical tractability. Our model is non-Markovian in that the next jump of the walker is (probabilistically) determined by the history of past jumps. It also has elements of intermittency in that one possibility at each step is that the walker does not move at all. This rich encompassing scenario arising from a single model provides useful insights into the source of different types of asymptotic behavior.
Kumar
Niraj
N
Department of Chemistry and Biochemistry, BioCircuits Institute, University of California-San Diego, La Jolla, 92093-0340, USA.
Harbola
Upendra
U
Lindenberg
Katja
K
D001704:Biopolymers / Q000737:chemistry*; D003198:Computer Simulation; D004058:Diffusion; D008390:Markov Chains; D008956:Models, Chemical; D008958:Models, Molecular; D015233:Models, Statistical
D001704:Biopolymers