The chaotic behavior, that gas-solid fluidization exhibits, has been characterized using the state space analysis. The space trajectories (attractor) of the dynamic system, reconstructed from the experimental time series of pressure fluctuations in the bed, have been described by the commonly used invariants: correlation dimension (CD), largest Lyapunov exponent (Ly) and the Kolmogorov entropy (K). The evolution of these invariants has been evaluated for bubbling, slugging and turbulent regime by analyzing the dependence on the flow regimes investigated. A new correlation has been proposed to predict the K for slugging regime. Due to some uncertainty involved in the delay determination for the attractor reconstruction, an attractor shape descriptor has been introduced. As shape descriptor, the dynamic moments of the attractor have been chosen and the morphological differences on the shape have been analyzed by varying the delay. The fluidization regimes have been characterized by the dynamic moments. (C) 2011 Elsevier Ltd. All rights reserved.