A Dynamical System with a Strange Attractor

Alexander A. Roytvarf

A chapter in Thinking in Problems, 2013, pp 43-53 from Springer

Abstract: Abstract This chapter contains real-life problems that can arise in the analysis of the dynamic behavior of a gradient algorithm for an iterative reconstruction in computerized tomography (CT). In most practical cases, the gradient algorithm apparently converges. However, the theory cannot exclude situations where its behavior becomes very complicated, even chaotic, depending on the parameters. Even in a simplified situation this algorithm may show some striking behavior! The simplified situation is related to the recursion formula $$ {x_0}>0, \quad \quad \quad \quad {x_{n+1 }}={x_n}\cdot {e^{{-({x_n}-\xi )}}} $$ (ξ ≥ 0 is the constant parameter); the asymptotic behavior of the sequence x n is governed by the parameter ξ. The reader is invited to investigate the behavior for 0

Keywords: Striking Behavior; Coordinate Substitution; Unique Local Extremum; Distinct Common Points; Distinct Simple Roots (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-0-8176-8406-8_5

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DOI: 10.1007/978-0-8176-8406-8_5

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