Two Lagrangian formulations for describing the damped harmonic oscillator have been introduced by Bateman. For these models we construct higher derivative generalizations which enjoy l-conformal Newton-Hooke symmetry. It is shown that dynamics of generalized systems corresponds to Pais-Uhlenbeck a particular choice its frequencies.

In 2011 Pehlivan proposed a three–dimensional forced–damped autonomous differential system which can display simultaneously unbounded and chaotic solutions. This untypical phenomenon has been studi...