NUMERICAL AND GEOMETRICAL ANALYSIS OF BIFURCATION AND CHAOS FOR AN ASYMMETRIC ELASTIC NONLINEAR OSCILLATOR

An asymmetric nonlinear oscillator representative of the finite forced dynamics of a structural system with initial curvature is used as a m odel system to show how the combined use of numerical and geometrical analysis allows deep insight into bifurcation phenomena and chaotic be haviour in the light of the system global dynamics. Numerical techniqu es are used to calculate fixed points of the response and bifurcation diagrams, to identify chaotic attractors, and to obtain basins of attr action of coexisting solutions. Geometrical analysis in control-phase portraits of the invariant manifolds of the direct and inverse saddles corresponding to unstable periodic motions is performed systematicall y in order to understand the global attractor structure and the attrac tor and basin bifurcations.