Deterministic Brownian-like Motion: Electronic Approach

Brownian motion is a dynamic behavior with random changes over time (stochastic) that occurs in many vital functions related to fluid environments, stock behavior, or even renewable energy generation. In this paper, we present a circuit implementation that reproduces Brownian motion based on a fully...

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Published in:Electronics (Basel) 2022-09, Vol.11 (18), p.2949
Main Authors: Echenausía-Monroy, José Luis, Campos, Eric, Jaimes-Reátegui, Rider, García-López, Juan Hugo, Huerta-Cuellar, Guillermo
Format: Article
Language:English
Subjects:
Approximation
Behavior
Brownian motion
Chemical reactions
Circuits
Design and construction
Differential equations
Eigenvalues
Electronic circuits
Equilibrium
Frequency spectrum
Normal distribution
Oscillators (Electronics)
Power law
Signal generation
Statistical analysis
Viscosity
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Summary:Brownian motion is a dynamic behavior with random changes over time (stochastic) that occurs in many vital functions related to fluid environments, stock behavior, or even renewable energy generation. In this paper, we present a circuit implementation that reproduces Brownian motion based on a fully deterministic set of differential equations. The dynamics of the electronic circuit are characterized using four well-known metrics of Brownian motion, namely: (i) Detrended Fluctuation Analysis (DFA), (ii) power law in the power spectrum, (iii) normal probability distribution, and (iv) Mean Square Displacement (MSD); where traditional Brownian motion exhibits linear time growth of the MSD, a Gaussian distribution, a −2 power law of the frequency spectrum, and DFA values close to 1.5. The obtained results show that for a certain combination of values in the deterministic model, the dynamics in the electronic circuit are consistent with the expectations for a stochastic Brownian behavior. The presented electronic circuit improves the study of Brownian behavior by eliminating the stochastic component, allowing reproducibility of the results through fully deterministic equations, and enabling the generation of physical signals (analog electronic signals) with Brownian-like properties with potential applications in fields such as medicine, economics, genetics, and communications, to name a few.
ISSN:2079-9292
2079-9292
DOI:10.3390/electronics11182949