Abstract
The paper introduces a method for reconstructing one-dimensional iterated maps that are driven by an external control input and subjected to an additive stochastic perturbation, from sequences of probability density functions that are generated by the stochastic dynamical systems and observed experimentally.
Highlights
There is considerable interest in modeling and analyzing dynamical systems that generate densities of states
This paper introduces for the first time a method to infer a onedimensional map that is driven by an external control input while being subjected to an additive stochastic perturbation from sequences of observed density functions generated by the unknown system
This paper introduced a new algorithm for reconstructing the underlying onedimensional map for an autonomous dynamical system that is driven by an additive control input and subjected to an additive stochastic perturbation, given the observed sequences of probability density functions generated by the unknown system, and the input and noise density functions
Summary
There is considerable interest in modeling and analyzing dynamical systems that generate densities of states. The problem of reconstructing an unknown onedimensional autonomous chaotic map given only knowledge of the invariant density function of the system has been considered by a number of authors (Ershov and Malinetskii 1988; Góra and Boyarsky 1993; Diakonos and Schmelcher 1996; Pingel et al 1999), while there are special cases in which this problem has a unique solution. To our knowledge, all existing methods consider only autonomous maps In this context, this paper introduces for the first time a method to infer a onedimensional map that is driven by an external control input while being subjected to an additive stochastic perturbation from sequences of observed density functions generated by the unknown system.
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