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Synthesizing chaotic maps with prescribed invariant densities |
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| Authors: | Alan Rogers Robert Shorten Daniel M. Heffernan |
| Affiliation: | aDepartment of Electronic Engineering, NUI Maynooth, Co. Kildare, Ireland bHamilton Institute, NUI Maynooth, Co. Kildare, Ireland cDepartment of Mathematical Physics, NUI Maynooth, Co. Kildare, Ireland |
| Abstract: | The Inverse Frobenius–Perron Problem (IFPP) concerns the creation of discrete chaotic mappings with arbitrary invariant densities. In this Letter, we present a new and elegant solution to the IFPP, based on positive matrix theory. Our method allows chaotic maps with arbitrary piecewise-constant invariant densities, and with arbitrary mixing properties, to be synthesized. |
| Keywords: | Chaos Chaotic maps Chaos control Inverse Frobenius–Perron problem |
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