POINCARE MAPS OF IMPULSED OSCILLATORS AND 2-DIMENSIONAL DYNAMICS

The Poincare map of one-dimensional linear oscillators subject to peri odic, non-linear and time-delayed impulses is shown to reduce to a fam ily of plane maps with possible non-uniqueness of the inverse. By rest ricting the analysis to a convenient form of the impulse function, a v ariety of interesting dynamical behaviours in this family are pointed out, including multistability and homoclinic bifurcations. Critical cu rves of two-dimensional endomorphisms are used to identify the structu re of absorbing areas and their bifurcations.