WIT Press

A Julia Set Methodology For The Detection Of Transient Chaotic Oscillations In Continuous Control Systems

Price

Free (open access)

Paper DOI

10.2495/AI960531

Volume

16

Pages

10

Published

1996

Size

168 kb

Author(s)

David W. Russell & James J. Alpigini

Abstract

The paper defines and demonstrates the occurrence of chaos in the iteration of mathematical formulae and shows that such systems can be exposed by their dependence on the initial values of variables and parametric coefficients. Filled Julia sets, although computationally intensive, give visual explanation of the fate of an iteration and indicate regions of crossover between stable and unstable operation. The paper then demonstrates that even the simplest process controllers may be subject to chaos in their component parts while still maintaining control of the primary outputs of the system. A variation on the Julia set is then described and offered as a possible \“chaotic function analyzer

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