EVENT DETAILS AND ABSTRACT

Title: An Operational Test for Distinguishing between Complicated and Chaotic Behavior in Deterministic Systems
Speaker: Professor M. Johnson
Speaker Info: Northwestern U.
Brief Description:
Special Note: Unusal time!!
Abstract:

While various definitions of chaotic processes have been proposed, there is not yet an established operational criterion for computing whether a given process is chaotic. We here use a diffusional measure to characterize whether a given deterministic process and domain is chaotic (operationally defined as exhibiting stochastic behavior). This technique introduces an additional coordinate linked to the process to be examined. By then determining the growth of the second moment of orbit trajectories in this added direction, it can be determined whether the process is chaotic. The process examined is analogous to Taylor dispersion whereby diffusion in the cross-sectional plane of a flow leads to diffusive-like dispersion in the axial direction. It is demonstrated that two other commonly used measures of chaos, a positive Lyapunov exponent or the autocorrelation coefficient dropping to zero, fail in certain cases to detect chaotic processes, but this new proposed test works in all of the cases examined. The cases include a number of standard mappings (logistic equation, trigonometic map, exponential map, Henon map) along with more recent work using the ABC flow. It will also be demonstrated (time-permitting) that this new criterion can be related to an entropic increase of a system.