Impacting oscillators - the problem of visualization of basins of attraction

Abstract

The objects of the investigations presented in this paper are two dynamical systems. The first one is a linear oscillator that can hit the immovable base; the second one consists of two linear oscillators that can impact on each other. For selected sets of parameters, various kinds of motion of these systems are possible: a motion without impacts (periodic or quasi-periodic) and a motion with impacts (periodic or chaotic). The kind of motion depends on initial conditions. The question arises then; what is the sensitivity of motion to external disturbances? The answer can be found by means of making the maps of basins of attraction of all existing attractors. Two examples of such maps and the differences between them caused by a various number of degrees of freedom of the systems under consideration are presented in this paper.