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Synthesis of piecewise-linear chaotic maps: Invariant densities, autocorrelations and switching
Rogers, Alan; Shorten, Robert N.; Heffernan, Daniel; Naughton, Thomas J.
In this paper, we give a review of the Inverse Frobenius–Perron problem (IFPP): how to create chaotic maps with desired invariant densities. After describing some existing methods for solving the IFPP, we present a new and simple matrix method of doing this. We show how the invariant density and the autocorrelation properties of the maps can be controlled independently. We also give some fundamental results on switching between a number of different chaotic maps and the effect this has on the overall invariant density of the system. The invariant density of the switched system can be controlled by varying the probabilities of choosing each individual map. Finally, we present an interesting application of the matrix method to image generation, by synthesizing a two-dimensional map, which when iterated, generates a well-known image.
Keyword(s): Computer Science; Mathematical Physics; Chaos; chaotic maps; chaos applications; Inverse Frobenius–Perron problem; IFPP
Publication Date:
Type: Journal article
Peer-Reviewed: Yes
Institution: Maynooth University
Citation(s): Rogers, Alan and Shorten, Robert N. and Heffernan, Daniel and Naughton, Thomas J. (2008) Synthesis of piecewise-linear chaotic maps: Invariant densities, autocorrelations and switching. International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, 18 (8). pp. 2169-2189. ISSN 0218-1274
Publisher(s): World Scientific Publishing
File Format(s): other
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First Indexed: 2014-09-20 05:01:10 Last Updated: 2018-08-31 06:26:49