Generalized multiplicative stochastic processes arising from one-dimensional maps with noise

We propose a class of generalized multiplicative stochastic processes obtained by introducing an endo-perspective into one-dimensional maps with additive noise. We define an internal state for the noisy dynamics of a given one-dimensional map and study its statistical behavior. We found intermittenc...

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Bibliographic Details
Published in:Artificial life and robotics 2023-02, Vol.28 (1), p.15-20
Main Authors: Haruna, Taichi, Nakajima, Kohei
Format: Article
Language:English
Subjects:
Artificial Intelligence
Computation by Abstract Devices
Computer Science
Control
Mechatronics
Original Article
Robotics
Stochastic processes
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Summary:We propose a class of generalized multiplicative stochastic processes obtained by introducing an endo-perspective into one-dimensional maps with additive noise. We define an internal state for the noisy dynamics of a given one-dimensional map and study its statistical behavior. We found intermittency characterized by two power-laws in the dynamics of the internal state for the logistic map and the BZ map with noise which exhibit different noise-induced phenomena, namely, noise-induced chaos and noise-induced order, respectively. We show that the power-laws can be explained in a unified way from the theory of generalized multiplicative stochastic processes.
ISSN:1433-5298
1614-7456
DOI:10.1007/s10015-022-00790-7