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

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Abstract

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.

Item Type:	Article
Keywords:	Chaos; chaotic maps; chaos applications; Inverse Frobenius–Perron problem; IFPP;
Academic Unit:	Faculty of Science and Engineering > Computer Science Faculty of Science and Engineering > Mathematical Physics
Item ID:	4786
Depositing User:	Prof. Daniel Heffernan
Date Deposited:	25 Feb 2014 12:17
Journal or Publication Title:	International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
Publisher:	World Scientific Publishing
Refereed:	Yes
URI:	Publisher
Use Licence:	This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here

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