Nonlinear Phenomena in Complex Systems, 2004, Vol.7, No.1, pp.1-16

NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
An Interdisciplinary Journal

2004, Vol.7, No.1, pp.1-16

Investigation of Transient Processes in One-Dimensional Maps.
A.E.Hramov, A.E.Khramova, I.A.Khromova, and A.A.Koronovskii

This paper presents the result of the investigation of transient process duration in one-dimensional dynamical systems with discrete time. Having considered a sample of one-dimensional map (the logistic map), we have shown that the mean duration of transient process is governed by the multiplicator of the stable cycle and proposed the equations, describing its dependence on computation accuracy. The mechanisms of complication of transient process duration dependence on initial conditions, with control parameter being increased, have been discussed. This paper also adduces some scaling laws taking place in one-dimensional dynamical systems with discrete time.
Key words: transient processes, nonlinear dynamics, dynamical system, scaling, initial conditions

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