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http://ipicyt.repositorioinstitucional.mx/jspui/handle/1010/1750| Nonclassical point of view of the Brownian motion generation via fractional deterministic model | |
| Héctor Eduardo Gilardi Velázquez Eric Campos Cantón | |
| En Embargo | |
| 31-12-2019 | |
| Atribución-NoComercial-SinDerivadas | |
| https://doi.org/10.1142/S0129183118500201 | |
| Fractional Brownian motion Deterministic Brownian motion Unstable dissipative systems DFA analysis | |
| "In this paper, we present a dynamical system based on the Langevin equation without stochastic term and using fractional derivatives that exhibit properties of Brownian motion, i.e. a deterministic model to generate Brownian motion is proposed. The stochastic process is replaced by considering an additional degree of freedom in the second-order Langevin equation. Thus, it is transformed into a system of three first-order linear differential equations, additionally α-fractional derivative are considered which allow us to obtain better statistical properties. Switching surfaces are established as a part of fluctuating acceleration. The final system of three α-order linear differential equations does not contain a stochastic term, so the system generates motion in a deterministic way. Nevertheless, from the time series analysis, we found that the behavior of the system exhibits statistics properties of Brownian motion, such as, a linear growth in time of mean square displacement, a Gaussian distribution. Furthermore, we use the detrended fluctuation analysis to prove the Brownian character of this motion." | |
| World Scientific | |
| 2018 | |
| Artículo | |
| H. E. Gilardi-Velázquez, and E. Campos-Cantón.(2018). Nonclassical point of view of the Brownian motion generation via fractional deterministic model. International Journal of Modern Physics CVol. 29, No. 03, 1850020 | |
| MATEMÁTICAS | |
| Versión revisada | |
| submittedVersion - Versión revisada | |
| Aparece en las colecciones: | Publicaciones Científicas Control y Sistemas Dinámicos |