Chaos in a Nonlinear Driven Oscillator with Exact Solution

Abstract

A nonlinear oscillator externally driven by an impulsive periodic force is investigated. An exact analytical expression is obtained for the stoboscopic or Poincar\'e map for all values of parameters. The model displays period-doubling sequences and chaotic behavior. The convergence rate of these cascades is in very good agreement with Feingenbaum theory.