Theoretical and Numerical Validation of the Stochastic Interrogation Experimental Method

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.

Theoretical and Numerical Validation of the Stochastic Interrogation Experimental Method

Stochastic interrogation is an experimental method that uses transient trajectories starting at numerous 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 interrogation experimental method is checked with the aid of a numerical model, using theoretical predictions from Melnikov theory and direct computations of invariant manifolds.