A stochastic interrogation method for experimental measurements of global dynamics and basin evolution: Application to a two-well oscillator

Abstract

An experimental study of local and global bifurcations in a driven two-well magneto-mechanical oscillator is presented. A detailed picture of the local bifurcation structure of the system is obtained using an automated bifurcation data acquisition system. Basins of attractions for the system are obtained using a new experimental technique: an ensemble of initial conditions is generated by switching between stochastic and deterministic excitation. Using this stochastic interrogation method, we observe the evolution of basins of attraction in the nonlinear oscillator as the forcing amplitude is increased, and find evidence for homoclinic bifurcation before the onset of chaos. Since the entire transient is collected for each initial condition, the same data can be used to obtain pictures of the flow of points in phase space. Using Liouville's Theorem, we obtain damping estimates by calculating the contraction of volumes under the action of the Poincare map, and show that they are in good agreement with the results of more conventional damping estimation methods. Finally, the stochastic interrogation data is used to estimate transition probability matrices for finite partitions of the Poincare section. Using these matrices, the evolution of probability densities can be studied.