Bifurcation structure at 1/3-subharmonic resonance in an asymmetric nonlinear elastic oscillator

The attractor-basin bifurcation structure in an asymmetric nonlinear oscillator representative of the planar finite forced dynamics of elastic structural systems with initial curvature is studied at the 1/3-subharmonic resonance regime. Local and global analyses are made by means of different computational tools to obtain frequency-response curves of coexisting regular solutions, bifurcation diagrams ensuing from different sets of initial conditions, manifolds structure of direct and inverse saddles corresponding to unstable periodic solutions, basins of attraction at different values of the control parameter. Deep insight into the global dynamics of the system and its evolution is achieved through the analysis of synthetic attractor-basin-manifold phase portraits. The topological mechanisms which entail onset and disappearance of various attractors, and the main and secondary evolutions to chaos, are identified. Special attention is devoted to the analysis of sudden bifurcational events characterizing the system global dynamics, associated with the topological behavior of the invariant manifolds of several direct and inverse saddles. Features of basin metamorphosis, attractor-basin accessibility, and window occurrence are examined. The approach followed, consisting in combined bifurcation analysis of the attractor-basin structure and of the manifold structure, is thought to be useful for a variety of dynamical systems.