An approach to generate deterministic Brownian motion

作者：Huerta Cuellar G^*; Jimenez Lopez E; Campos Canton E; Pisarchik A N

来源：Communications in Nonlinear Science & Numerical Simulation, 2014, 19(8): 2740-2746.

DOI：10.1016/j.cnsns.2014.01.010

• Brownian motion
• Deterministic Brownian motion
• Unstable dissipative systems
• DFA analysis

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.

• 出版日期2014-8