Controlling nonlinear dynamics in a two-well impact system. II. Attractorsand bifurcation scenario under unsymmetric optimal excitation

To exploit all potentialities of the optimal control procedure, the analysi s initiated in Part I focuses on the system response under one-side control , an excitation which furnishes high gain though, roughly, controlling only one part of the phase space. Many bifurcational and control items related to the unsymmetric and pulsed nature of the excitation are deeply investiga ted. A nonclassical kind of homoclinic bifurcation is identified and it is discussed how it may lead to major regularity. The system response is very rich, and the main local and global phenomena of the dynamics are analyzed in detail through combined use of bifurcation diagrams and attractor-basin phase portraits. Both the confinement of steady dynamics in the controlled potential well and their successive transition from confined to scattered a re studied, and it is discussed how they are related to the left and right homoclinic bifurcations. The performances of each control are obtained thro ugh comparison with the case of harmonic excitation. It is shown that the t wo investigated optimal excitations permit to increase the amplitude level for confined to scattered dynamics and to regularize the steady dynamics, a lthough in a different manner. The analysis shows the effectiveness - in "a verage" sense - of the proposed method for controlling nonlinear dynamics.