Abstract
In many practical situations, it is impossible to measure the individual trajectories generated by an unknown chaotic system, but we can observe the evolution of probability density functions generated by such a system. The paper proposes for the first time a matrix-based approach to solve the generalized inverse Frobenius–Perron problem, that is, to reconstruct an unknown one-dimensional chaotic transformation, based on a temporal sequence of probability density functions generated by the transformation. Numerical examples are used to demonstrate the applicability of the proposed approach and evaluate its robustness with respect to constantly applied stochastic perturbations.
Highlights
One-dimensional chaotic maps describe many dynamical processes, encountered in engineering, biology, X
The problem of inferring an unknown chaotic map given the invariant density generated by the map is known as the inverse Frobenius–Perron problem (IFPP)
This paper has addressed in a systematic manner the problem of inferring one-dimensional chaotic maps based on sequences of probability density functions
Summary
One-dimensional chaotic maps describe many dynamical processes, encountered in engineering, biology, X. The problem of inferring an unknown chaotic map given the invariant density generated by the map is known as the inverse Frobenius–Perron problem (IFPP). The realization of nonlinear dynamical automata that describe cognitive processes based on experimental data can be formulated as an inverse Frobenius–Perron problem Another major limitation of the existing matrixbased reconstruction algorithms is the assumption that the Markov partition is known in advance. Our approach provides for the first time a solution to the problem of inferring, from sequences of density functions, a broad class of onedimensional transformations that admit an invariant density when the Markov partition is not known in advance.
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