114 research outputs found
Predictive dynamical and stochastic systems
We study a system whose dynamics are governed by predictions of its future
states. A general formalism and concrete examples are presented. We find that
the dynamical characteristics depend on how to shape the predictions as well as
on how far ahead in time to make them. We also report that noise can induce
oscillatory behavior, which we call "predictive stochastic resonance".Comment: Presented and To appear in the Proc. of 9th Granada Seminar,
(Granada, Spain, September 11-15, 2006
Quantum Square Well Bound States Described by Equations with Non-locality
We present here a simple equation explicitly incorporating non-locality,
which reproduces quantized energy levels of the bound states for the square
well potentials. Introduction of this equation is motivated by studies of
differential equation with time delayed feedback, which can be viewed as
describing temporal non-locality.Comment: 4 pages, 1 figure, submitted for a publicatio
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