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