Phys. Rev. E 52, 3277–3280 (1995)Delayed random walksReceived 14 March 1995; published in the issue dated September 1995 The fluctuations about the stable point in a delayed dynamical system are modeled as a delayed random walk: i.e., a random walk in which the transition probability depends on the position of the walker at a time τ in the past and transitions in the direction of the stable point are more probable. It is shown that, depending on the magnitude of the delay, the root mean square displacement √〈X2(t)〉 versus time interval approaches a limiting value in either an oscillatory or nonoscillatory fashion. This limiting value of √〈X2(t)〉 is a linear function of τ. © 1995 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevE.52.3277
DOI:
10.1103/PhysRevE.52.3277
PACS:
87.10.+e
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