Nonclassical point of view of the Brownian motion generation via fractional deterministic model
"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...
| Autores: | , |
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| Formato: | artículo |
| Estado: | Versión enviada para evaluación y publicación |
| Fecha de publicación: | 2018 |
| País: | México |
| Recursos: | Instituto Potosino de Investigación Científica y Tecnológica |
| Repositorio: | Repositorio Institucional del IPICYT |
| OAI Identifier: | oai:ipicyt.repositorioinstitucional.mx:1010/1750 |
| Acesso em linha: | http://ipicyt.repositorioinstitucional.mx/jspui/handle/1010/1750 |
| Access Level: | acceso embargado |
| Palavra-chave: | info:eu-repo/classification/Autor/Fractional Brownian motion info:eu-repo/classification/Autor/Deterministic Brownian motion info:eu-repo/classification/Autor/Unstable dissipative systems info:eu-repo/classification/Autor/DFA analysis info:eu-repo/classification/cti/1 info:eu-repo/classification/cti/12 |
| Resumo: | "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." |
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