Spatio-temporal dimensionality in the overall complex dynamics of an experimental cable/mass system

An experimental model of an elastic cable/mass hanging at in-phase or out-of-phase vertically moving supports is considered. System parameters are adjusted to produce two different conditions of multiple internal resonance. Nonregular dynamics are analyzed in various frequency ranges including meaningful external resonance conditions. Attention is devoted to characterization of system dimensionality in terms of both time and spatial complexity. The aims of this paper are (i) to give a general overview of the richness and robustness of different (quasiperiodic and homoclinic) bifurcation scenarios to chaos in various regions of the control parameter space, (ii) to characterize steady nonregular response through delay-embedding technique for attractor reconstruction and proper orthogonal decomposition of spatio-temporal flow and (iii) to identify spatial configuration variables (experimental eigenfunctions) contributing mostly to nonregular dynamics, thus obtaining hints about possible reduced models for reproducing complex regimes. System dimensionality will be evaluated both by relating the dimension of attractors to the dimension of the linear phase space, and from the dominating proper orthogonal modes.