7 February 2007 Variations of piece-wise liner 1D one-parameter chaotic map
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Probability properties of one-dimensional piece-wise linear chaotic map having two linear brunches (Rényi map) are investigated. The map dynamics depends on a parameter defining substantially view of the map, i.e. slopes of map linear branches and proportion between them. This dependence is very sensitive, and there is the infinite set of parameter values providing existence of piecewise constant invariant density of the map. These values of the parameter may be obtained by solving corresponding algebraic equation. These properties allow us to apply the map for modeling complex chaotic regimes by means of switching between various values of parameter. The map is suggested to be suitable for description of degrees of chaotic neuron reactions on weak excitations and for chaotic encryption.
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Valery M. Anikin, Valery M. Anikin, Alexander S. Remizov, Alexander S. Remizov, Sergey S. Arkadaksky, Sergey S. Arkadaksky, } "Variations of piece-wise liner 1D one-parameter chaotic map", Proc. SPIE 6436, Complex Dynamics and Fluctuations in Biomedical Photonics IV, 64360L (7 February 2007); doi: 10.1117/12.699886; https://doi.org/10.1117/12.699886

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