An approach to generate deterministic Brownian motion

• We propose a new approach for the generation of deterministic Brownian motion.
• Additional degree of freedom to the Langevin equation instead of the stochastic term.
• Brownian motion can be achieved by using a unstable dissipative system.
• Detrended fluctuation analysis shows that Brownian motion is generated.
• Brownian motion is related to the microscopic chaos in fluids.

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.