Basins of Attraction

This research considers a global behavior aspect of nonlinear systems - basins of attraction in systems exhibiting bi-stability. Mapping out the final destination of a grid of initial conditions in numerical simulation is quite straightforward. Experimentally, it is much more challenging. However, a system can be subject to a random sequence of disturbances, and making use of a few techniques from nonlinear dyanmics allows a systems dependence on initial conditions to be examined. The following are simply colorful examples, but they can be cross-referenced back to the appropriate publications, listed to the right.

The important point of this research is that (in contrast to linear systems) nonlinear systems are capable of exhibiting long-term recurrent behavior that depends on where the system was started from, and in some cases this dependence on initial conditions is extremely sensitive.

One of the key engineering contexts for basins of attraction is found in the buckling behavior of slender axially-compressed structures:

Here is an example of a repeatedly and randomly perturbed system with three co-existing attractors:

Repeatedly and randomly perturbed system with co-existing attrcators


Here are basins of attraction from various mechanical experiments:

Duffing cart/track:

 Morphing basins in a link model:


And some basins for an impact-frcition oscillator: