Gluing bifurcation and noise-induced hopping in the oscillatory phenomena of compartmentalized bidisperse granular gases.

Oscillatory phenomena of compartmentalized bidisperse granular gases are studied through experiments, molecular dynamics simulations, and a flux model [Mikkelsen et al., Phys. Rev. E 70, 061307 (2004)]. The degenerate oscillatory state (d-OSC), which has been predicted in our previous simulations [Liu et al., Phys. Rev. E 79, 052301 (2009)], is experimentally observed and well described by the flux model. From the d-OSC state, the system takes a transition to a complete oscillatory state (OSC) through a homoclinic gluing bifurcation. Around the bifurcation point, noise-induced periodic irregularity is observed, and it can be perfectly reproduced by simulations and the flux model with additional random flux terms. The numerical results show a low-frequency divergence characteristic of the irregular oscillation, which is clearly caused by noise-induced hopping between OSC and d-OSC states.