This talk will involve the intersection of several advanced mathematical studies.|
Nonlinear dynamics is ubiquitous to the real world. Though a sensitive dependence on initial conditions implies that we cannot fully predict the result of chaotic systems, the study of pattern formation tells us that we can at least predict the type of result. The existence of symmetry in a system further limits the range of possible solutions. However, in the real world, this is complicated by another ubiquitous presence, noise. When noise shifts those sensitive conditions throughout the whole system, deterministic chaos is out the window. Or is it?
Recently, constructive effects of noise have been discovered. Our numerical simulations of cellular flame behavior have always fallen short of real world behaviors that have been observed in the laboratory. When a small stochastic term is added to the Kuramoto-Sivashinsky equation, some of those strange behaviors are observed numerically. The speaker will attempt to explain why this makes sense, and shed some light on what happens when sensitive dependence meets constant perturbation.