An asymmetric nonlinear oscillator representative of the finite forced dynamics of a structural system with initial curvature is used as a model system to show how the combined use of numerical and geometrical analysis allows deep insight into bifurcation phenomena and chaotic behaviour in the light of the system global dynamics. Numerical techniques are used to calculate fixed points of the response and bifurcation diagrams, to identify chaotic attractors, and to obtain basins of attraction 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 systematically in order to understand the global attractor structure and the attractor and basin bifurcations.
NUMERICAL AND GEOMETRICAL ANALYSIS OF BIFURCATION AND CHAOS FOR AN ASYMMETRIC ELASTIC NONLINEAR OSCILLATOR / Rega, Giuseppe; A., Salvatori; F., Benedettini. - In: NONLINEAR DYNAMICS. - ISSN 0924-090X. - STAMPA. - 7:2(1995), pp. 249-272. (Intervento presentato al convegno Workshop on Bifurcation and Chaos in Mechanical SYstems tenutosi a LAQUILA, ITALY nel MAY 19-20, 1992) [10.1007/bf00053711].
NUMERICAL AND GEOMETRICAL ANALYSIS OF BIFURCATION AND CHAOS FOR AN ASYMMETRIC ELASTIC NONLINEAR OSCILLATOR
REGA, GIUSEPPE;
1995
Abstract
An asymmetric nonlinear oscillator representative of the finite forced dynamics of a structural system with initial curvature is used as a model system to show how the combined use of numerical and geometrical analysis allows deep insight into bifurcation phenomena and chaotic behaviour in the light of the system global dynamics. Numerical techniques are used to calculate fixed points of the response and bifurcation diagrams, to identify chaotic attractors, and to obtain basins of attraction 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 systematically in order to understand the global attractor structure and the attractor and basin bifurcations.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
