Theoretical and Numerical Validation of the Stochastic Interrogation Experimental Method

Abstract

Stochastic interrogation is an experimental method that uses transient trajectories starting at nu merous pseudo-random initial conditions to obtain detailed information about the flow of a dynamical system in phase space. From this flow information, various global dynamical phenomena can be studied, such as the transition to complex basin boundaries, chaotic transients, and strange non-attracting sets. The existence of these features in turn allows the occurrence of a homoclinic bifurcation to be inferred, even when all attractors in a system are nonchaotic. In this paper, the validity of inferences made using the stochastic in terrogation experimental method is checked with the aid of a numerical model, using theoretical predictions from Melnikov theory and direct computations of invariant manifolds.