Bifurcation and nonlinear behavior of compartmentalized granular gases

Abstract

Different from the molecular gas, clustering is a most commonly observed feature of the granular gas. A review is given of our previous work on the clustering, especially the oscillatory clustering for shaken fluidized granular matter in connected compartments, as examples for pattern formation and bifurcations in far from equilibrium systems. Flux model is presented and discussed for mono-disperse and bi-disperse granular systems. Comparison of the flux model with simulation results is given. They show reasonably well agreements. Besides the homogeneous (HOM), segregation (SEG), and oscillatory (OSC) states, two new stationary states (d-OSC and s-HOM) in the bi-disperse granular system are predicted by our simulation. In our recent work these two new states are observed experimentally, and their flow diagrams are obtained based on the flux model. The transition from degenerate oscillation state to oscillation state demonstrates a homoclinic gluing bifurcation.

Bifurcations Induced in a Bistable Oscillator via Joint Noises and Time Delay

“…The occurrence of bifurcation was first introduced by Henri Poincaré [1885]. Since then, the investigation of bifurcation has attracted extensive attention and it has been utilized in many fields [Hou et al, 2014;Jost, 2014], including neuronal networks [Djeundam et al, 2013;Tian et al, 2015], biological systems [Bi et al, 2014;Liu, 2015], and biochemistry [Zang et al, 2015].…”