An approach to generate deterministic Brownian motion |
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| Affiliation: | 1. Universidad Autónoma de Nuevo León, Av. Pedro de Alba s/n, Cd. Universitaria, C.P. 66451 San Nicolás de los Garza, Nuevo León, Mexico;2. Centro de Investigación Científica y de Educación Superior de Ensenada, Carretera Ensenada-Tijuana No. 3918, Zona Playitas, C.P. 22860 Ensenada, B.C., Mexico;3. Universidad Autónoma de Baja California, Carretera Tijuana-Ensenada Km. 103, 22860 Ensenada, B.C., Mexico;1. Centro Universitario de los Lagos, Enrique Díaz de León 1144, Paseos de la Montaña, Lagos de Moreno 47460, Jalisco, Mexico;2. Center for Biomedical Technology, Technical University of Madrid, Campus Montegancedo, Pozuelo de Alarcon, Madrid 28223, Spain;3. Centro de Investigaciones en Óptica, Loma del Bosque 115, Lomas del Campestre, Leon, Guanajuato 37150, Mexico |
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| Abstract: | We propose an approach for generation of deterministic Brownian motion. By adding an additional degree of freedom to the Langevin equation and transforming it into a system of three linear differential equations, we determine the position of switching surfaces, which act as a multi-well potential with a short fluctuation escape time. Although the model is based on the Langevin equation, the final system does not contain a stochastic term, and therefore the obtained motion is deterministic. Nevertheless, the system behavior exhibits important characteristic properties of Brownian motion, namely, a linear growth in time of the mean square displacement, a Gaussian distribution, and a −2 power law of the frequency spectrum. Furthermore, we use the detrended fluctuation analysis to prove the Brownian character of this motion. |
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| Keywords: | Brownian motion Deterministic Brownian motion Unstable dissipative systems DFA analysis |
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