Bifurcation analysis of bubble dynamics in fluidized beds.

We use a low-dimensional, agent-based bubble model to study the changes in the global dynamics of fluidized beds in response to changes in the frequency of the rising bubbles. The computationally based bifurcation analysis shows that at low frequencies, the global dynamics is attracted towards a fixed point since the bubbles interact very little with one another. As the frequency of injection increases, however, the global dynamics undergoes a series of bifurcations to new behaviors that include highly periodic orbits, chaotic attractors, and intermittent behavior between periodic orbits and chaotic sets. Using methods from time-series analysis, we are able to approximate nonlinear models that allow for long-term predictions and the possibility of developing control algorithms.