A Stochastic Approach to the Construction of One-Dimensional Chaotic Maps with Prescribed Statistical Properties

F. K. Diakonos; D. Pingel; P. Schmelcher

doi:10.1016/s0375-9601(99)00775-6

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arXiv · chao-dyn/9910020

A Stochastic Approach to the Construction of One-Dimensional Chaotic Maps with Prescribed Statistical Properties

F. K. Diakonos·D. Pingel·P. Schmelcher

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Abstract

We use a recently found parametrization of the solutions of the inverse Frobenius-Perron problem within the class of complete unimodal maps to develop a Monte-Carlo approach for the construction of one-dimensional chaotic dynamical laws with given statistical properties, i.e. invariant density and autocorrelation function. A variety of different examples are presented to demonstrate the power of our method.

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F. K. Diakonos, D. Pingel, P. Schmelcher. 1999-10-14. A Stochastic Approach to the Construction of One-Dimensional Chaotic Maps with Prescribed Statistical Properties. https://doi.org/10.1016/s0375-9601(99)00775-6

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