Butterflies and bifurcations in surface radio-frequency traps: The diversity of routes to chaos.

In the present article, we investigate the charged micro-particle dynamics in the surface radio-frequency trap (SRFT). We have developed a new configuration of the SRFT that consists of three curved electrodes on a glass substrate for massive micro-particles trapping. We provide the results of numerical simulations for the dynamical regimes of charged silica micro-particles in the SRFT. Here, we introduce a term of a "main route" to chaos, i.e., the sequence of dynamical regimes for the given particles with the increase of the strength of an electric field. Using the Lyapunov exponent formalism, typical Reynolds number map, Poincaré sections, bifurcation diagrams, and attractor basin boundaries, we have classified three typical main routes to chaos depending on the particle size. Interestingly, in the system described here, all main scenarios of a transition to chaos are implemented, including the Feigenbaum scenario, the Landau-Ruelle-Takens-Newhouse scenario as well as intermittency.