Distinguishing periodic and chaotic time series obtained from an experimental nonlinear pendulum

The experimental analysis of nonlinear dynamical systems furnishes a scalar sequence of measurements, which may be analyzed using state space reconstruction and other techniques related to nonlinear analysis. The noise contamination is unavoidable in cases of data acquisition and, therefore, it is important to recognize techniques that can be employed for a correct identification of chaos. The present contribution discusses the experimental analysis of a nonlinear pendulum, considering state space reconstruction, frequency domain analysis and the determination of dynamical invariants, Lyapunov exponents and attractor dimension. A procedure to construct Poincare map of the signal is presented. The analyses of periodic and chaotic motions are carried out in order to establish a difference between them. Results show that it is possible to distinguish periodic and chaotic time series obtained from an experimental set up employing proper procedures even though noise suppression is not contemplated.